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If an employee's income is ₹60,000, the amount he spends is 50% higher than his savings. Therefore, his savings (in ₹) is:
यदि एक कर्मचारी की आय ₹60,000 है, और उसके द्वारा खर्च की गई राशि उसकी बचत से 50% अधिक है। तो उसकी बचत (₹ में) क्या है?
(A) (a) ₹20,000
(B) (b) ₹24,000
(C) (c) ₹25,000
(D) (d) ₹28,000
✅ Answer & Explanation
Sahi jawab: B) (b) ₹24,000Explanation: Method 1 (Ratio Method): Expenditure savings se $50\% = \frac{1}{2}$ adhik hai. Savings : Expenditure $= 2 : (2 + 1) = 2 : 3$. Total Income $=$ Savings $+$ Expenditure $= 2 + 3 = 5$ units. Given: 5 units $= ₹60000 \implies 1 \text{ unit} = \frac{60000}{5} = ₹12000$. Savings = 2 units $= 2 \times 12000 = ₹24000$. Atah sahi vikalp (b) ₹24,000 hai. Method 2 (100-Base Method): Savings ko $100$ maan lo. Expenditure $= 100 + 50 = 150$. Total Income $= 100 + 150 = 250$. Savings fraction of income $= \frac{100}{250} = \frac{2}{5}$. Savings $= \frac{2}{5} \times 60000 = 2 \times 12000 = ₹24000$. Atah sahi uttar (b) hai.
Total savings of P and Q is 30% of their total income. Their average expenditure is ₹28,000. What is the total salary of P and Q?
P और Q की कुल बचत उनकी कुल आय का 30% है। उनका औसत खर्च ₹28,000 है। P और Q का कुल वेतन क्या है?
(A) (a) ₹70,000
(B) (b) ₹75,000
(C) (c) ₹80,000
(D) (d) ₹85,000
✅ Answer & Explanation
Sahi jawab: C) (c) ₹80,000Explanation: Method 1 (Ratio Method): Total Savings $= 30\% = \frac{3}{10}$ of Total Income. Total Expenditure $= 1 - \frac{3}{10} = \frac{7}{10}$ of Total Income. Average expenditure ₹28,000 hai, isliye total expenditure $= 28000 \times 2 = ₹56000$. 7 units $= ₹56000 \implies 1 \text{ unit} = \frac{56000}{7} = ₹8000$. Total Income (10 units) $= 10 \times 8000 = ₹80000$. Atah sahi vikalp (c) ₹80,000 hai. Method 2 (100-Base Method): Total income $= 100\%$. Total savings $= 30\% \implies$ Total expenditure $= 100\% - 30\% = 70\%$. Total Expenditure $= 2 \times 28000 = ₹56000$. $70\% = ₹56000$. $1\% = \frac{56000}{70} = ₹800$. Total Income ($100\%$) $= 800 \times 100 = ₹80000$. Atah sahi uttar (c) hai.
Aman saves 25% of his monthly salary. When his expenses are increased by 20%, he is able to save ₹3,000 per month. His monthly salary is:
अमन अपने मासिक वेतन का 25% बचाता है। जब उसके खर्चों में 20% की वृद्धि होती है, तो वह प्रति माह ₹3,000 बचाने में सक्षम होता है। उसका मासिक वेतन क्या है?
(A) (a) ₹25,000
(B) (b) ₹28,000
(C) (c) ₹30,000
(D) (d) ₹32,000
✅ Answer & Explanation
Sahi jawab: C) (c) ₹30,000Explanation: Method 1 (Ratio Method): Let Salary $= 100$ units. Initial Savings $= 25$ units, Expenses $= 75$ units. Expenses increase by $20\% \implies 75 + (20\% \text{ of } 75) = 75 + 15 = 90$ units. New Savings $= 100 - 90 = 10$ units. Given: 10 units $= ₹3000 \implies 1 \text{ unit} = ₹300$. Monthly Salary (100 units) $= 100 \times 300 = ₹30000$. Atah sahi vikalp (c) ₹30,000 hai. Method 2 (100-Base Method): Income $= 100\%$. Initial Expenses $= 75\%$, Savings $= 25\%$. New Expenses $= 75\% \times 1.20 = 90\%$. New Savings $= 100\% - 90\% = 10\%$. Given: $10\% = ₹3000 \implies 100\% = ₹30000$. Atah sahi uttar (c) hai.
The income of A is 20% more than that of B. A got a 20% rise in his income, and B got a 30% rise in his income. The percentage increase in their combined income is:
A की आय B की आय से 20% अधिक है। A की आय में 20% की वृद्धि हुई, और B की आय में 30% की वृद्धि हुई। उनकी संयुक्त आय में प्रतिशत वृद्धि क्या है?
(A) (a) 23.54%
(B) (b) 24.55%
(C) (c) 25.00%
(D) (d) 26.25%
✅ Answer & Explanation
Sahi jawab: B) (b) 24.55%Explanation: Method 1 (Ratio / Weighted Average Method): $20\% = \frac{1}{5} \implies$ B ki income $= 5$ units, A ki income $= 6$ units. Combined initial income $= 6 + 5 = 11$ units. Rise in A's income $= 6 \times 20\% = 1.2$ units. Rise in B's income $= 5 \times 30\% = 1.5$ units. Total rise $= 1.2 + 1.5 = 2.7$ units. Percentage increase in combined income: $= \frac{2.7}{11} \times 100\% = \frac{270}{11}\% \approx 24.55\%$. Atah sahi vikalp (b) 24.55% hai. Method 2 (100-Base Method): B ki income $= 100$ maan lo, A ki income $= 120$. Combined income initially $= 100 + 120 = 220$. New income of A $= 120 + 24 = 144$. New income of B $= 100 + 30 = 130$. New combined income $= 144 + 130 = 274$. Combined increase $= 274 - 220 = 54$. Percentage increase $= \frac{54}{220} \times 100\% = \frac{270}{11}\% \approx 24.55\%$. Atah sahi uttar (b) hai.
Aman spends 80% of his income. If his income increases by 25% and his expenditure also increases by 15%, how much percent will Aman's savings increase?
अमन अपनी आय का 80% खर्च करता है। यदि उसकी आय में 25% की वृद्धि होती है और उसके खर्च में भी 15% की वृद्धि होती है, तो अमन की बचत में कितने प्रतिशत की वृद्धि होगी?
(A) (a) 55%
(B) (b) 60%
(C) (c) 65%
(D) (d) 70%
✅ Answer & Explanation
Sahi jawab: C) (c) 65%Explanation: Method 1 (100-Base Method): Initial Income $= 100$ maan lete hain. Expenditure $= 80$, Savings $= 100 - 80 = 20$. Income me $25\%$ hike $\implies$ New Income $= 125$. Expenditure me $15\%$ hike $\implies 80 + (15\% \text{ of } 80) = 80 + 12 = 92$. New Savings $= 125 - 92 = 33$. Savings me increase $= 33 - 20 = 13$ units (20 ke base par). Percentage increase in savings $= \frac{13}{20} \times 100\% = 65\%$. Atah sahi vikalp (c) 65% hai. Method 2 (Ratio / Allegation Method): Expenditure : Savings $= 80 : 20 = 4 : 1$. Overall Income increase $= 25\%$, Expenditure increase $= 15\%$. Savings increase ko $x\%$ maan lo: $1 \times (x - 25) = 4 \times (25 - 15) \implies x - 25 = 40 \implies x = 65\%$. Atah sahi uttar (c) hai.
The ratio of Priya's expenditure and savings is 3:2. If her income and expenditure increase by 25% and 15% respectively, find the percentage increase in her savings.
प्रिया के खर्च और बचत का अनुपात 3:2 है। यदि उसकी आय और खर्च में क्रमशः 25% और 15% की वृद्धि होती है, तो उसकी बचत में प्रतिशत वृद्धि ज्ञात कीजिए।
(A) (a) 35%
(B) (b) 40%
(C) (c) 42%
(D) (d) 45%
✅ Answer & Explanation
Sahi jawab: B) (b) 40%Explanation: Method 1 (100-Base Scaling Method): Expenditure $= 300$, Savings $= 200 \implies$ Total Income $= 500$. Income increase ($25\%$): $500 + 125 = 625$. Expenditure increase ($15\%$): $300 + 45 = 345$. New Savings $= 625 - 345 = 280$. Savings me increase $= 280 - 200 = 80$ units (200 ke base par). Percentage increase in savings $= \frac{80}{200} \times 100\% = 40\%$. Atah sahi vikalp (b) 40% hai. Method 2 (Weighted Average / Allegation): Expenditure : Savings $= 3 : 2$. Let savings growth be $S\%$. $\frac{3 \times 15 + 2 \times S}{3 + 2} = 25 \implies 45 + 2S = 125 \implies 2S = 80 \implies S = 40\%$. Atah sahi uttar (b) hai.
A woman spends 3/4 of her income. If her income increases by 20% and the expenditure increases by 16%, then the percentage increase in her savings will be:
एक महिला अपनी आय का 3/4 भाग खर्च करती है। यदि उसकी आय में 20% की वृद्धि होती है और खर्च में 16% की वृद्धि होती है, तो उसकी बचत में प्रतिशत वृद्धि क्या होगी?
(A) (a) 28%
(B) (b) 30%
(C) (c) 32%
(D) (d) 35%
✅ Answer & Explanation
Sahi jawab: C) (c) 32%Explanation: Method 1 (Ratio Method): Total Income $= 400$ units maan lo. Expenditure $= \frac{3}{4} \times 400 = 300$ units. Savings $= 400 - 300 = 100$ units. New Income ($+20\%$): $400 + 80 = 480$. New Expenditure ($+16\%$): $300 + 48 = 348$. New Savings $= 480 - 348 = 132$. Savings 100 se 132 ho gayi, yaani direct increase $= 132 - 100 = 32\%$. Atah sahi vikalp (c) 32% hai. Method 2 (Deviation / Allegation Method): Expenditure weight $= 3$, Savings weight $= 1$. Total Income deviation $= 20\%$. $1 \times (\text{Savings}\% - 20) = 3 \times (20 - 16) = 12$. $\text{Savings}\% = 20 + 12 = 32\%$. Atah sahi uttar (c) hai.
The proportion of Mohan's spending to saving is 4:1. His salary rises by 20%. What percentage of his expenditure will increase if his saving grows by 12%?
मोहन के खर्च और बचत का अनुपात 4:1 है। उसके वेतन में 20% की वृद्धि होती है। यदि उसकी बचत में 12% की वृद्धि होती है, तो उसके खर्च में कितने प्रतिशत की वृद्धि होगी?
(A) (a) 20%
(B) (b) 22%
(C) (c) 24%
(D) (d) 25%
✅ Answer & Explanation
Sahi jawab: B) (b) 22%Explanation: Method 1 (100-Base Method): Spending $= 400$, Saving $= 100 \implies$ Total Salary $= 500$. Salary increase ($20\%$): $500 + 100 = 600$. Saving increase ($12\%$): $100 + 12 = 112$. New Spending $= 600 - 112 = 488$. Spending me badhav $= 488 - 400 = 88$ units (400 ke base par). Percentage increase $= \frac{88}{400} \times 100\% = 22\%$. Atah sahi vikalp (b) 22% hai. Method 2 (Weighted Average Method): Spending : Saving $= 4 : 1$. Let expenditure increase be $E\%$. $\frac{4 \times E + 1 \times 12}{4 + 1} = 20 \implies 4E + 12 = 100 \implies 4E = 88 \implies E = 22\%$. Atah sahi uttar (b) hai.
Karan spends 75% of his income. His income increases by 20% and his expenditure also increases by 8%. The percentage increase in his savings is:
करण अपनी आय का 75% खर्च करता है। उसकी आय में 20% की वृद्धि होती है और उसके खर्च में भी 8% की वृद्धि होती है। उसकी बचत में प्रतिशत वृद्धि क्या है?
(A) (a) 50%
(B) (b) 54%
(C) (c) 56%
(D) (d) 60%
✅ Answer & Explanation
Sahi jawab: C) (c) 56%Explanation: Method 1 (100-Base Method): Initial Income $= 100$. Expenditure $= 75$, Savings $= 100 - 75 = 25$. New Income ($+20\%$) $= 120$. New Expenditure ($+8\%$) $= 75 + (8\% \text{ of } 75) = 75 + 6 = 81$. New Savings $= 120 - 81 = 39$. Increase in Savings $= 39 - 25 = 14$ units (25 ke base par). Percentage increase $= \frac{14}{25} \times 100\% = 56\%$. Atah sahi vikalp (c) 56% hai. Method 2 (Allegation Method): Expenditure : Savings $= 75 : 25 = 3 : 1$. Let savings increase be $S\%$. $1 \times (S - 20) = 3 \times (20 - 8) \implies S - 20 = 36 \implies S = 56\%$. Atah sahi uttar (c) hai.
Rohit spends 60% of his income. His income increased by 20% and his expenditure increased by 10%. What is the percentage increase in his savings?
रोहित अपनी आय का 60% खर्च करता है। उसकी आय में 20% की वृद्धि हुई और उसके खर्च में 10% की वृद्धि हुई। उसकी बचत में प्रतिशत वृद्धि क्या है?
(A) (a) 30%
(B) (b) 32%
(C) (c) 35%
(D) (d) 36%
✅ Answer & Explanation
Sahi jawab: C) (c) 35%Explanation: Method 1 (100-Base Method): Initial Income $= 100$. Expenditure $= 60$, Savings $= 100 - 60 = 40$. New Income ($+20\%$) $= 120$. New Expenditure ($+10\%$) $= 60 + 6 = 66$. New Savings $= 120 - 66 = 54$. Savings me increase $= 54 - 40 = 14$ units (40 ke base par). Percentage increase $= \frac{14}{40} \times 100\% = 35\%$. Atah sahi vikalp (c) 35% hai. Method 2 (Ratio / Weighted Average Method): Expenditure : Savings $= 60 : 40 = 3 : 2$. Total Income growth $= 20\%$, Expenditure growth $= 10\%$. $\frac{3 \times 10 + 2 \times S}{5} = 20 \implies 30 + 2S = 100 \implies 2S = 70 \implies S = 35\%$. Atah sahi uttar (c) hai.
Vikas spends 70% of his income. His income is increased by 30% and he increases his expenditure by 20%. By what percentage are his savings increased?
विकास अपनी आय का 70% खर्च करता है। उसकी आय में 30% की वृद्धि होती है और वह अपने खर्च में 20% की वृद्धि करता है। उसकी बचत में कितने प्रतिशत की वृद्धि होगी?
(A) (a) 50.00%
(B) (b) 53.33%
(C) (c) 55.00%
(D) (d) 56.67%
✅ Answer & Explanation
Sahi jawab: B) (b) 53.33%Explanation: Method 1 (100-Base Method): Initial Income $= 100$. Expenditure $= 70$, Savings $= 30$. New Income ($+30\%$) $= 130$. New Expenditure ($+20\%$) $= 70 + 14 = 84$. New Savings $= 130 - 84 = 46$. Savings me increase $= 46 - 30 = 16$ units (30 ke base par). Percentage increase $= \frac{16}{30} \times 100\% = \frac{160}{3}\% = 53.33\%$. Atah sahi vikalp (b) 53.33% hai. Method 2 (Ratio Method): Expenditure : Savings $= 7 : 3$. Total Income growth $= 30\%$, Expenditure growth $= 20\%$. $\frac{7 \times 20 + 3 \times S}{10} = 30 \implies 140 + 3S = 300 \implies 3S = 160 \implies S = 53.33\%$. Atah sahi uttar (b) hai.
Sumit spends 85% of his income. His income increased by 20%, while his spending rose by 10%. The percentage increase in his savings is:
सुमित अपनी आय का 85% खर्च करता है। उसकी आय में 20% की वृद्धि हुई, जबकि उसके खर्च में 10% की वृद्धि हुई। उसकी बचत में प्रतिशत वृद्धि क्या है?
(A) (a) 65.50%
(B) (b) 72.33%
(C) (c) 76.67%
(D) (d) 80.00%
✅ Answer & Explanation
Sahi jawab: C) (c) 76.67%Explanation: Method 1 (100-Base Method): Initial Income $= 100$. Spending $= 85$, Savings $= 100 - 85 = 15$. New Income ($+20\%$) $= 120$. New Spending ($+10\%$) $= 85 + 8.5 = 93.5$. New Savings $= 120 - 93.5 = 26.5$. Savings me increase $= 26.5 - 15 = 11.5$ units (15 ke base par). Percentage increase $= \frac{11.5}{15} \times 100\% = \frac{23}{3}\% = 76.67\%$. Atah sahi vikalp (c) 76.67% hai. Method 2 (Ratio / Weighted Average Method): Spending : Savings $= 85 : 15 = 17 : 3$. Let savings rise be $S\%$. $\frac{17 \times 10 + 3 \times S}{20} = 20 \implies 170 + 3S = 400 \implies 3S = 230 \implies S = 76.67\%$. Atah sahi uttar (c) hai.
Kavita spends 60% of her income. Her income increases by 20% and her expenditure increases by 10%. By what percentage does her saving increase?
कविता अपनी आय का 60% खर्च करती है। उसकी आय में 20% की वृद्धि होती है और उसके खर्च में 10% की वृद्धि होती है। उसकी बचत में कितने प्रतिशत की वृद्धि होगी?
(A) (a) 30%
(B) (b) 35%
(C) (c) 40%
(D) (d) 25%
✅ Answer & Explanation
Sahi jawab: B) (b) 35%Explanation: Method 1 (100-Base Method): Initial Income $= 100$ maan lete hain. Expenditure $= 60$, Savings $= 100 - 60 = 40$. New Income ($+20\%$) $= 120$. New Expenditure ($+10\%$) $= 60 + 6 = 66$. New Savings $= 120 - 66 = 54$. Savings me increase $= 54 - 40 = 14$ units (40 ke base par). Percentage increase in savings $= \frac{14}{40} \times 100\% = 35\%$. Atah sahi vikalp (b) 35% hai. Method 2 (Ratio / Allegation Method): Expenditure : Savings $= 60 : 40 = 3 : 2$. Overall Income growth $= 20\%$, Expenditure growth $= 10\%$. Let savings growth be $S\%$. $\frac{3 \times 10 + 2 \times S}{3 + 2} = 20 \implies 30 + 2S = 100 \implies 2S = 70 \implies S = 35\%$. Atah sahi uttar (b) hai.
Dinesh spends 70% of his income. If his income is increased by 20% and his expenditure is increased by 10%, then the percentage increase in the savings of Dinesh will be:
दिनेश अपनी आय का 70% खर्च करता है। यदि उसकी आय में 20% की वृद्धि होती है और उसके खर्च में 10% की वृद्धि होती है, तो दिनेश की बचत में प्रतिशत वृद्धि क्या होगी?
(A) (a) 40.00%
(B) (b) 43.33%
(C) (c) 45.00%
(D) (d) 50.00%
✅ Answer & Explanation
Sahi jawab: B) (b) 43.33%Explanation: Method 1 (100-Base Method): Initial Income $= 100$. Expenditure $= 70$, Savings $= 100 - 70 = 30$. New Income ($+20\%$) $= 120$. New Expenditure ($+10\%$) $= 70 + 7 = 77$. New Savings $= 120 - 77 = 43$. Savings me increase $= 43 - 30 = 13$ units (30 ke base par). Percentage increase $= \frac{13}{30} \times 100\% = \frac{130}{3}\% \approx 43.33\%$. Atah sahi vikalp (b) 43.33% hai. Method 2 (Ratio Method): Expenditure : Savings $= 7 : 3$. Total Income rise $= 20\%$, Expenditure rise $= 10\%$. Let savings growth be $S\%$. $7 \times 10 + 3 \times S = 10 \times 20 \implies 70 + 3S = 200 \implies 3S = 130 \implies S = 43.33\%$. Atah sahi uttar (b) hai.
Pooja saves 25% of her income. If her income is increased by 20% and she saves 30% of the new income, by what percentage will her actual savings increase?
पूजा अपनी आय का 25% बचाती है। यदि उसकी आय में 20% की वृद्धि होती है और वह नई आय का 30% बचाती है, तो उसकी वास्तविक बचत में कितने प्रतिशत की वृद्धि होगी?
(A) (a) 40%
(B) (b) 44%
(C) (c) 48%
(D) (d) 50%
✅ Answer & Explanation
Sahi jawab: B) (b) 44%Explanation: Method 1 (100-Base Method): Initial Income $= 100$ maan lo. Initial Savings $= 25\% \text{ of } 100 = 25$. New Income ($+20\%$) $= 120$. New Savings $= 30\% \text{ of } 120 = 0.30 \times 120 = 36$. Savings me increase $= 36 - 25 = 11$ units (25 ke base par). Percentage increase in savings $= \frac{11}{25} \times 100\% = 44\%$. Atah sahi vikalp (b) 44% hai. Method 2 (Ratio Multiplier Method): Initial savings $= 100 \times 0.25 = 25$. New savings $= 100 \times 1.20 \times 0.30 = 36$. Initial : New Savings $= 25 : 36$. Increase $= 36 - 25 = 11$ units. Percentage increase $= \frac{11}{25} \times 100\% = 44\%$. Atah sahi uttar (b) hai.
Manish could save 25% of his income. But 3 years later, when his income increased by 20%, he could save the same amount of money as before. By how much percentage did his expenditure increase?
मनीष अपनी आय का 25% बचा सकता था। लेकिन 3 वर्ष बाद, जब उसकी आय में 20% की वृद्धि हुई, तो वह पहले जितनी ही राशि बचा सका। उसके खर्च में कितने प्रतिशत की वृद्धि हुई?
(A) (a) 25.00%
(B) (b) 26.67%
(C) (c) 28.50%
(D) (d) 30.00%
✅ Answer & Explanation
Sahi jawab: B) (b) 26.67%Explanation: Method 1 (100-Base Method): Initial Income $= 100$. Initial Savings $= 25$, Initial Expenditure $= 100 - 25 = 75$. New Income ($+20\%$) $= 120$. Bachat pehle ke barabar hi hai $\implies$ New Savings $= 25$. New Expenditure $= 120 - 25 = 95$. Expenditure me increase $= 95 - 75 = 20$ units (75 ke base par). Percentage increase in expenditure $= \frac{20}{75} \times 100\% = \frac{4}{15} \times 100\% = 26.67\%$. Atah sahi vikalp (b) 26.67% hai. Method 2 (Ratio Method): Initial Income : Savings : Expenditure $= 4 : 1 : 3$. Scale by 25: Income $= 100$, Savings $= 25$, Expenditure $= 75$. Income ho gayi 120, savings rahi 25, toh kharch ho gaya 95. Increase in expenditure $= \frac{95 - 75}{75} \times 100\% = \frac{20}{75} \times 100\% = 26.67\%$. Atah sahi uttar (b) hai.
Sunil spends 50% of his income on household items. If his income increases by 30% and his expenditure increases by 10%, then find the percentage change in his savings.
सुनील अपनी आय का 50% घरेलू वस्तुओं पर खर्च करता है। यदि उसकी आय में 30% की वृद्धि होती है और उसके खर्च में 10% की वृद्धि होती है, तो उसकी बचत में प्रतिशत परिवर्तन ज्ञात कीजिए।
(A) (a) 40% increase
(B) (b) 45% increase
(C) (c) 50% increase
(D) (d) 55% increase
✅ Answer & Explanation
Sahi jawab: C) (c) 50% increaseExplanation: Method 1 (100-Base Method): Initial Income $= 100$. Expenditure $= 50$, Savings $= 50$. New Income ($+30\%$) $= 130$. New Expenditure ($+10\%$) $= 50 + 5 = 55$. New Savings $= 130 - 55 = 75$. Savings me increase $= 75 - 50 = 25$ units (50 ke base par). Percentage increase $= \frac{25}{50} \times 100\% = 50\%$. Atah sahi vikalp (c) 50% increase hai. Method 2 (Direct Weighted Relation): Kyunki Expenditure aur Savings dono barabar ($1 : 1$) hain: $\text{Income growth} = \frac{\text{Exp growth} + \text{Sav growth}}{2}$ $30\% = \frac{10\% + S}{2} \implies 10\% + S = 60\% \implies S = 50\%$. Atah sahi uttar (c) hai.
The monthly income of a person is ₹20,000 and his expenditure is ₹15,000. Next year, his income increases by 20% but his expenditure decreases by 10%. The percentage increase in his savings is:
एक व्यक्ति की मासिक आय ₹20,000 है और उसका खर्च ₹15,000 है। अगले वर्ष, उसकी आय में 20% की वृद्धि होती है लेकिन उसके खर्च में 10% की कमी आती है। उसकी बचत में प्रतिशत वृद्धि क्या है?
(A) (a) 100%
(B) (b) 110%
(C) (c) 120%
(D) (d) 125%
✅ Answer & Explanation
Sahi jawab: B) (b) 110%Explanation: Method 1 (Absolute Value Method): Initial Savings $= 20000 - 15000 = ₹5000$. New Income ($+20\%$) $= 20000 + 4000 = ₹24000$. New Expenditure ($-10\%$) $= 15000 - 1500 = ₹13500$. New Savings $= 24000 - 13500 = ₹10500$. Increase in savings $= 10500 - 5000 = ₹5500$. Percentage increase $= \frac{5500}{5000} \times 100\% = 110\%$. Atah sahi vikalp (b) 110% hai. Method 2 (Ratio Method): Income : Expenditure : Savings $= 20000 : 15000 : 5000 = 4 : 3 : 1$. Base scale: Income $= 400$, Exp $= 300$, Sav $= 100$. New Income ($+20\%$) $= 480$. New Exp ($-10\%$) $= 270$. New Sav $= 480 - 270 = 210$. Savings increase $= 210 - 100 = 110\%$. Atah sahi uttar (b) hai.
The ratio of expenditure to savings of a woman is 3:1. If her income and expenditure are increased by 20% and 12%, respectively, then find the percentage change in her savings.
एक महिला के खर्च और बचत का अनुपात 3:1 है। यदि उसकी आय और खर्च में क्रमशः 20% और 12% की वृद्धि होती है, तो उसकी बचत में प्रतिशत परिवर्तन ज्ञात कीजिए।
(A) (a) 40%
(B) (b) 44%
(C) (c) 48%
(D) (d) 36%
✅ Answer & Explanation
Sahi jawab: B) (b) 44%Explanation: Method 1 (100-Base Scaling Method): Expenditure $= 300$, Savings $= 100 \implies$ Total Income $= 400$. New Income ($+20\%$) $= 400 + 80 = 480$. New Expenditure ($+12\%$) $= 300 + 36 = 336$. New Savings $= 480 - 336 = 144$. Savings me increase $= 144 - 100 = 44$ units (100 ke base par). Percentage change $= 44\%$ increase. Atah sahi vikalp (b) 44% hai. Method 2 (Deviation / Allegation Method): Expenditure weight $= 3$, Savings weight $= 1$. Average income growth $= 20\%$. $1 \times (S - 20) = 3 \times (20 - 12) \implies S - 20 = 24 \implies S = 44\%$. Atah sahi uttar (b) hai.
The monthly income of Amit in 2022 was ₹24,000 and his monthly expenditure was ₹16,000. In 2023, his income increased by 25% and his expenditure increased by 10%. Find the percentage increase in his savings.
वर्ष 2022 में अमित की मासिक आय ₹24,000 थी और उसका मासिक खर्च ₹16,000 था। वर्ष 2023 में उसकी आय में 25% और खर्च में 10% की वृद्धि हुई। उसकी बचत में प्रतिशत वृद्धि ज्ञात कीजिए।
(A) (a) 50%
(B) (b) 55%
(C) (c) 60%
(D) (d) 45%
✅ Answer & Explanation
Sahi jawab: B) (b) 55%Explanation: Method 1 (Ratio Method): Initial Income : Expenditure : Savings $= 24000 : 16000 : 8000 = 3 : 2 : 1$. Base scale: Income $= 300$, Exp $= 200$, Sav $= 100$. New Income ($+25\%$) $= 300 + 75 = 375$. New Exp ($+10\%$) $= 200 + 20 = 220$. New Savings $= 375 - 220 = 155$. Increase in savings $= 155 - 100 = 55\%$. Atah sahi vikalp (b) 55% hai. Method 2 (Absolute Value Method): Initial savings $= 24000 - 16000 = ₹8000$. New Income $= 24000 + 6000 = ₹30000$. New Expenditure $= 16000 + 1600 = ₹17600$. New Savings $= 30000 - 17600 = ₹12400$. Savings increase $= 12400 - 8000 = ₹4400$. Percentage increase $= \frac{4400}{8000} \times 100\% = 55\%$. Atah sahi uttar (b) hai.
Vipin's expenditure and savings are in the ratio of 4:1. His income increases by 20%. If his savings increase by 15%, then by how much percentage does his expenditure increase?
विपिन के खर्च और बचत का अनुपात 4:1 है। उसकी आय में 20% की वृद्धि होती है। यदि उसकी बचत में 15% की वृद्धि होती है, तो उसके खर्च में कितने प्रतिशत की वृद्धि होगी?
(A) (a) 20.25%
(B) (b) 21.25%
(C) (c) 22.50%
(D) (d) 24.00%
✅ Answer & Explanation
Sahi jawab: B) (b) 21.25%Explanation: Method 1 (100-Base Scaling Method): Expenditure $= 400$, Savings $= 100 \implies$ Total Income $= 500$. Income increase ($20\%$): $500 + 100 = 600$. Savings increase ($15\%$): $100 + 15 = 115$. New Expenditure $= 600 - 115 = 485$. Expenditure me badhav $= 485 - 400 = 85$ units (400 ke base par). Percentage increase $= \frac{85}{400} \times 100\% = 21.25\%$. Atah sahi vikalp (b) 21.25% hai. Method 2 (Weighted Average Method): Expenditure : Savings $= 4 : 1$. Let expenditure increase be $E\%$. $\frac{4 \times E + 1 \times 15}{5} = 20 \implies 4E + 15 = 100 \implies 4E = 85 \implies E = 21.25\%$. Atah sahi uttar (b) hai.
The monthly expenditure of a person is 50% more than his monthly savings. If his monthly income increases by 30% and monthly expenditure increases by 40%, then he saves ₹1,500 more in a month. What is his initial monthly expenditure (in ₹)?
एक व्यक्ति का मासिक खर्च उसकी मासिक बचत से 50% अधिक है। यदि उसकी मासिक आय में 30% और मासिक खर्च में 40% की वृद्धि होती है, तो वह प्रति माह ₹1,500 अधिक बचाता है। उसका प्रारंभिक मासिक खर्च (₹ में) क्या है?
(A) (a) ₹12,000
(B) (b) ₹15,000
(C) (c) ₹18,000
(D) (d) ₹22,500
✅ Answer & Explanation
Sahi jawab: B) (b) ₹15,000Explanation: Method 1 (Ratio Scaling Method): Expenditure savings se $50\% = \frac{1}{2}$ zyada hai $\implies$ Savings $= 200$ units, Expenditure $= 300$ units. Initial Income $= 200 + 300 = 500$ units. New Income ($+30\%$): $500 + 150 = 650$ units. New Expenditure ($+40\%$): $300 + 120 = 420$ units. New Savings $= 650 - 420 = 230$ units. Savings me increase $= 230 - 200 = 30$ units. Given: 30 units $= ₹1500 \implies 1 \text{ unit} = \frac{1500}{30} = ₹50$. Initial Expenditure = 300 units $= 300 \times 50 = ₹15,000$. Atah sahi vikalp (b) ₹15,000 hai. Method 2 (Algebraic Formulation): Let initial savings $= 2x$, expenditure $= 3x$, income $= 5x$. New income $= 5x \times 1.30 = 6.5x$. New expenditure $= 3x \times 1.40 = 4.2x$. New savings $= 6.5x - 4.2x = 2.3x$. Increase in savings $= 2.3x - 2x = 0.3x$. Given: $0.3x = 1500 \implies x = 5000$. Initial Expenditure $= 3x = 3 \times 5000 = ₹15,000$. Atah sahi uttar (b) hai.
Raghu used to spend 75% of his income. His income has increased by 15%, and he increases his expenditure by 10%. If Raghu earlier saved y and after the increases he now saves x, then what is the value of ((x - y) / y * 100)%?
रघु अपनी आय का 75% खर्च करता था। उसकी आय में 15% की वृद्धि हुई है, और वह अपने खर्च में 10% की वृद्धि करता है। यदि रघु पहले y बचाता था और वृद्धि के बाद अब वह x बचाता है, तो ((x - y) / y * 100)% का मान क्या है?
(A) (a) 25%
(B) (b) 28%
(C) (c) 30%
(D) (d) 32%
✅ Answer & Explanation
Sahi jawab: C) (c) 30%Explanation: Method 1 (100-Base Method): $\left(\frac{x - y}{y} \times 100\right)\%$ ka matlab seedhe savings ka percentage increase nikalna hai. Initial Income $= 100$. Initial Expenditure $= 75$, Initial Savings ($y$) $= 100 - 75 = 25$. New Income ($+15\%$) $= 115$. New Expenditure ($+10\%$) $= 75 + 7.5 = 82.5$. New Savings ($x$) $= 115 - 82.5 = 32.5$. Savings increase $= x - y = 32.5 - 25 = 7.5$. Percentage increase $= \frac{7.5}{25} \times 100\% = 30\%$. Atah sahi vikalp (c) 30% hai. Method 2 (Ratio Method): Expenditure : Savings $= 75 : 25 = 3 : 1$. Overall Income rise $= 15\%$, Expenditure rise $= 10\%$. $1 \times (S - 15) = 3 \times (15 - 10) \implies S - 15 = 15 \implies S = 30\%$. Atah sahi uttar (c) hai.
A person saves 40% of his income. Next year, his income increases by 150%. He increases his savings by four times the previous year's savings. By what percentage has his expenditure decreased?
एक व्यक्ति अपनी आय का 40% बचाता है। अगले वर्ष, उसकी आय में 150% की वृद्धि होती है। वह अपनी बचत में पिछले वर्ष की बचत के चार गुना की वृद्धि करता है। उसके खर्च में कितने प्रतिशत की कमी आई है?
(A) (a) 12.50%
(B) (b) 15.00%
(C) (c) 16.67%
(D) (d) 20.00%
✅ Answer & Explanation
Sahi jawab: C) (c) 16.67%Explanation: Method 1 (100-Base Method): Initial Income $= 100$. Initial Savings $= 40$, Initial Expenditure $= 100 - 40 = 60$. New Income ($+150\%$) $= 100 + 150 = 250$. Savings me increase pichli savings ka 4 guna hai $\implies \text{Increase} = 4 \times 40 = 160$. New Savings $= 40 + 160 = 200$. New Expenditure $= 250 - 200 = 50$. Expenditure me kami $= 60 - 50 = 10$ units (60 ke base par). Percentage decrease $= \frac{10}{60} \times 100\% = \frac{1}{6} \times 100\% = 16.67\%$. Atah sahi vikalp (c) 16.67% hai. Method 2 (Ratio Balance Method): Base ratio: Savings $= 2$, Expenditure $= 3$, Income $= 5$. New Income $= 5 \times 2.5 = 12.5$. Savings increase $= 2 \times 4 = 8 \implies$ New Savings $= 2 + 8 = 10$. New Expenditure $= 12.5 - 10 = 2.5$. Expenditure me kami $= 3 - 2.5 = 0.5$ units. Percentage decrease $= \frac{0.5}{3} \times 100\% = 16.67\%$. Atah sahi uttar (c) hai.
Tina used to save 25% of her income. If her income went up by 20%, while her expenditure went up by 30%, her nominal saving went down by ₹500. Find Tina's initial income (in ₹).
टीना अपनी आय का 25% बचाती थी। यदि उसकी आय में 20% की वृद्धि हुई, जबकि उसके खर्च में 30% की वृद्धि हुई, तो उसकी नाममात्र बचत में ₹500 की कमी आई। टीना की प्रारंभिक आय (₹ में) ज्ञात कीजिए।
(A) (a) ₹18,000
(B) (b) ₹20,000
(C) (c) ₹22,500
(D) (d) ₹25,000
✅ Answer & Explanation
Sahi jawab: B) (b) ₹20,000Explanation: Method 1 (100-Base Method): Initial Income $= 100$ units. Savings $= 25$ units, Expenditure $= 75$ units. New Income ($+20\%$) $= 120$ units. New Expenditure ($+30\%$) $= 75 + 22.5 = 97.5$ units. New Savings $= 120 - 97.5 = 22.5$ units. Decrease in Savings $= 25 - 22.5 = 2.5$ units. Given: 2.5 units $= ₹500 \implies 1 \text{ unit} = ₹200$. Initial Income (100 units) $= 100 \times 200 = ₹20000$. Atah sahi vikalp (b) ₹20,000 hai. Method 2 (Ratio Method): Income : Savings : Expenditure $= 400 : 100 : 300$. New Income $= 480$, New Expenditure $= 390$. New Savings $= 480 - 390 = 90$. Savings drop $= 100 - 90 = 10$ units. 10 units $= ₹500 \implies 1 \text{ unit} = ₹50$. Initial Income = 400 units $= 400 \times 50 = ₹20000$. Atah sahi uttar (b) hai.
A person earns ₹20,000 per month and spends 75% of his income and saves the remaining amount. If his income increases by 25% and expenditure by 10%, find the percentage of increase in his savings.
एक व्यक्ति प्रति माह ₹20,000 कमाता है और अपनी आय का 75% खर्च करता है तथा शेष राशि बचाता है। यदि उसकी आय में 25% और खर्च में 10% की वृद्धि होती है, तो उसकी बचत में प्रतिशत वृद्धि ज्ञात कीजिए।
(A) (a) 50%
(B) (b) 60%
(C) (c) 70%
(D) (d) 75%
✅ Answer & Explanation
Sahi jawab: C) (c) 70%Explanation: Method 1 (100-Base Method): Actual value (₹20,000) ka use kiye bina direct 100 base par solve kar sakte hain: Initial Income $= 100$. Expenditure $= 75$, Savings $= 25$. New Income ($+25\%$) $= 125$. New Expenditure ($+10\%$) $= 75 + 7.5 = 82.5$. New Savings $= 125 - 82.5 = 42.5$. Increase in savings $= 42.5 - 25 = 17.5$ units (25 ke base par). Percentage increase $= \frac{17.5}{25} \times 100\% = 70\%$. Atah sahi vikalp (c) 70% hai. Method 2 (Deviation / Allegation Method): Expenditure : Savings $= 75 : 25 = 3 : 1$. Total Income growth $= 25\%$, Expenditure growth $= 10\%$. $1 \times (S - 25) = 3 \times (25 - 10) \implies S - 25 = 45 \implies S = 70\%$. Atah sahi uttar (c) hai.
The ratio between the monthly income and the expenditure of Varun is 7:4. If his income increases by 25% and his expenditure increases by 20%, then find the percentage increase in his savings.
वरुण की मासिक आय और खर्च के बीच का अनुपात 7:4 है। यदि उसकी आय में 25% और उसके खर्च में 20% की वृद्धि होती है, तो उसकी बचत में प्रतिशत वृद्धि ज्ञात कीजिए।
(A) (a) 28.55%
(B) (b) 30.00%
(C) (c) 31.67%
(D) (d) 33.33%
✅ Answer & Explanation
Sahi jawab: C) (c) 31.67%Explanation: Method 1 (100-Base Scaling Method): Income $= 700$, Expenditure $= 400$. Savings $= 700 - 400 = 300$. New Income ($+25\%$): $700 + 175 = 875$. New Expenditure ($+20\%$): $400 + 80 = 480$. New Savings $= 875 - 480 = 395$. Savings me increase $= 395 - 300 = 95$ units (300 ke base par). Percentage increase $= \frac{95}{300} \times 100\% = \frac{95}{3}\% \approx 31.67\%$. Atah sahi vikalp (c) 31.67% hai. Method 2 (Weighted Average Method): Expenditure : Savings $= 4 : 3$. Total Income increase $= 25\%$, Expenditure increase $= 20\%$. $\frac{4 \times 20 + 3 \times S}{7} = 25 \implies 80 + 3S = 175 \implies 3S = 95 \implies S = 31.67\%$. Atah sahi uttar (c) hai.
A man spends 70% of his income. His income increases by 10% and his expenditure by 5%. What is the percentage increase in his savings?
एक व्यक्ति अपनी आय का 70% खर्च करता है। उसकी आय में 10% और उसके खर्च में 5% की वृद्धि होती है। उसकी बचत में कितने प्रतिशत की वृद्धि होगी?
(A) (a) 21.67%
(B) (b) 31.67%
(C) (c) 41.67%
(D) (d) 51.67%
✅ Answer & Explanation
Sahi jawab: A) (a) 21.67%Explanation: Method 1 (100-Base Method): Initial Income $= 100$ maan lete hain. Expenditure $= 70$, Savings $= 100 - 70 = 30$. New Income ($+10\%$) $= 110$. New Expenditure ($+5\%$) $= 70 + 3.5 = 73.5$. New Savings $= 110 - 73.5 = 36.5$. Savings me increase $= 36.5 - 30 = 6.5$ units (30 ke base par). Percentage increase $= \frac{6.5}{30} \times 100\% = \frac{65}{3}\% \approx 21.67\%$. Atah sahi vikalp (a) 21.67% hai. Method 2 (Alligation / Weighted Average Method): Expenditure : Savings $= 70 : 30 = 7 : 3$. Total income growth $= 10\%$, Expenditure growth $= 5\%$. Let savings growth be $S\%$. $\frac{7 \times 5 + 3 \times S}{10} = 10 \implies 35 + 3S = 100 \implies 3S = 65 \implies S = 21.67\%$. Atah sahi uttar (a) hai.
Mr. X has a monthly income of ₹26,500 and his monthly expenditure is ₹20,500. The next year, his salary is increased by 12% and expenditure is increased by 6%. His savings increase by how much percent?
श्रीमान X की मासिक आय ₹26,500 है और उनका मासिक खर्च ₹20,500 है। अगले वर्ष, उनके वेतन में 12% और खर्च में 6% की वृद्धि होती है। उनकी बचत में कितने प्रतिशत की वृद्धि होगी?
(A) (a) 32.5%
(B) (b) 27.3%
(C) (c) 32.0%
(D) (d) 34.7%
✅ Answer & Explanation
Sahi jawab: A) (a) 32.5%Explanation: Method 1 (Ratio Method): Initial Income : Expenditure : Savings $= 26500 : 20500 : 6000 = 53 : 41 : 12$. Income increase $= 53 \times 12\% = 6.36$ units. Expenditure increase $= 41 \times 6\% = 2.46$ units. Savings increase $= 6.36 - 2.46 = 3.90$ units. Percentage increase in savings $= \frac{3.90}{12} \times 100\% = \frac{390}{12}\% = 32.5\%$. Atah sahi vikalp (a) 32.5% hai. Method 2 (Absolute Value Method): Initial savings $= 26500 - 20500 = ₹6000$. Income increase $= 12\% \text{ of } 26500 = ₹3180$. Expenditure increase $= 6\% \text{ of } 20500 = ₹1230$. Increase in savings $= 3180 - 1230 = ₹1950$. Percentage increase $= \frac{1950}{6000} \times 100\% = 32.5\%$. Atah sahi uttar (a) hai.
A spends 65% of his income. His income is increased by 20.1% and the expenditure is increased by 20%. By what percent (correct to one decimal place) does his saving increase or decrease?
A अपनी आय का 65% खर्च करता है। उसकी आय में 20.1% की वृद्धि होती है और खर्च में 20% की वृद्धि होती है। उसकी बचत में कितने प्रतिशत की वृद्धि या कमी होती है (एक दशमलव स्थान तक सही)?
(A) (a) Decrease by 18.9%
(B) (b) Increase by 20.3%
(C) (c) Decrease by 17.7%
(D) (d) Increase by 21.5%
✅ Answer & Explanation
Sahi jawab: B) (b) Increase by 20.3%Explanation: Method 1 (100-Base Method): Initial Income $= 100$. Expenditure $= 65$, Savings $= 100 - 65 = 35$. New Income $= 100 + 20.1 = 120.1$. New Expenditure $= 65 + (20\% \text{ of } 65) = 65 + 13 = 78$. New Savings $= 120.1 - 78 = 42.1$. Savings me increase $= 42.1 - 35 = 7.1$ units (35 ke base par). Percentage increase $= \frac{7.1}{35} \times 100\% = \frac{142}{7}\% \approx 20.285\% \approx 20.3\%$ increase. Atah sahi vikalp (b) Increase by 20.3% hai. Method 2 (Ratio / Weighted Average Method): Expenditure : Savings $= 65 : 35 = 13 : 7$. Total Income growth $= 20.1\%$, Expenditure growth $= 20\%$. $\frac{13 \times 20 + 7 \times S}{20} = 20.1 \implies 260 + 7S = 402 \implies 7S = 142 \implies S \approx 20.3\%$ increase. Atah sahi uttar (b) hai.