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What percent of ₹400 is ₹72?
₹400 का कितना प्रतिशत ₹72 है?
(A) (a) 16%
(B) (b) 18%
(C) (c) 20%
(D) (d) 22%
✅ Answer & Explanation
Sahi jawab: B) (b) 18%Explanation: Method 1 (Ratio Method): Required Ratio = $\frac{72}{400} = \frac{9}{50}$. Since standard unit fraction $\frac{1}{50} = 2\%$, Value = $9 \times 2\% = 18\%$. Hence, correct option is (b) 18%. Method 2 (100-Base Scaling Method): Base quantity $400 = 100\%$. Divide both sides by 4 to bring the base directly to 100: $100 = 25\%$. Now for ₹72: $\frac{72}{4}\% = 18\%$. Hence, correct answer is (b).
If 75% of a number is 108, what is the number?
यदि किसी संख्या का 75% मान 108 है, तो वह संख्या क्या है?
(A) (a) 140
(B) (b) 148
(C) (c) 144
(D) (d) 152
✅ Answer & Explanation
Sahi jawab: C) (c) 144Explanation: Method 1 (Ratio Method): $75\% = \frac{3}{4}$. Here, 3 units $= 108 \implies 1 \text{ unit} = \frac{108}{3} = 36$. Original base number = 4 units $= 4 \times 36 = 144$. Hence, correct option is (c) 144. Method 2 (100-Base Method): $75\% \implies 108$. Divide by 3 to find $25\%$: $25\% = \frac{108}{3} = 36$. Multiply by 4 to get the complete number ($100\%$): $100\% = 36 \times 4 = 144$. Hence, correct answer is (c).
Which of the following is the least?
निम्नलिखित में से सबसे छोटा कौन सा है?
(A) (a) 16% of 550
(B) (b) 25% of 360
(C) (c) 30% of 280
(D) (d) 40% of 205
✅ Answer & Explanation
Sahi jawab: D) (d) 40% of 205Explanation: Method 1 (Ratio Conversion Method): • Option (a): $\frac{4}{25} \times 550 = 4 \times 22 = 88$ • Option (b): $25\% = \frac{1}{4} \implies \frac{1}{4} \times 360 = 90$ • Option (c): $\frac{3}{10} \times 280 = 3 \times 28 = 84$ • Option (d): $\frac{2}{5} \times 205 = 2 \times 41 = 82$ Comparing all values: $82 < 84 < 88 < 90$. Hence, the least value is (d) 40% of 205. Method 2 (10-Base Multiplier Method): • (a) $10\% = 55$, $6\% = 33 \implies 55 + 33 = 88$ • (b) $50\% = 180 \implies 25\% = 90$ • (c) $10\% = 28 \implies 30\% = 28 \times 3 = 84$ • (d) $10\% = 20.5 \implies 40\% = 20.5 \times 4 = 82$ Lowest value is 82, which corresponds to option (d).
If 15% of 35% of x is 315, then x = ?
यदि x के 35% का 15% मान 315 है, तो x = ?
(A) (a) 6000
(B) (b) 60000
(C) (c) 8000
(D) (d) 80000
✅ Answer & Explanation
Sahi jawab: B) (b) 60000Explanation: Method 1 (Ratio Method): $15\% = \frac{3}{20}$, $35\% = \frac{7}{20}$. Effective fraction $= \frac{3}{20} \times \frac{7}{20} = \frac{21}{400}$. Given: $\frac{21}{400} \times x = 315$. 21 units $= 315 \implies 1 \text{ unit} = \frac{315}{21} = 15$. Original value ($x$) = 400 units $= 400 \times 15 = 6000$ (Wait, $315 / 0.0525 = 6000$). Let's verify: $0.15 \times 0.35 \times x = 0.0525x = 315 \implies x = \frac{315}{0.0525} = 6000$. Hence, option (a) 6000 is correct. Method 2 (100-Base Method): Assume $x = 100\%$. $15\% \text{ of } 35\% = 5.25\%$. $5.25\% = 315 \implies 1\% = 60$. $100\% = 60 \times 100 = 6000$. Hence, correct answer is (a).
If 35% of 60% of a number is 63, then what is the number?
यदि किसी संख्या के 60% का 35% मान 63 है, तो वह संख्या क्या है?
(A) (a) 250
(B) (b) 300
(C) (c) 350
(D) (d) 400
✅ Answer & Explanation
Sahi jawab: B) (b) 300Explanation: Method 1 (Ratio Method): $35\% = \frac{7}{20}$, $60\% = \frac{3}{5}$. Combined product ratio $= \frac{7}{20} \times \frac{3}{5} = \frac{21}{100}$. Here, 21 units $= 63 \implies 1 \text{ unit} = 3$. Total number = 100 units $= 100 \times 3 = 300$. Hence, correct option is (b) 300. Method 2 (100-Base Method): Assume the number is 100. $60\% \text{ of } 100 = 60$. $35\% \text{ of } 60 = 21$. Now, $21\% = 63 \implies 1\% = \frac{63}{21} = 3$. Original number ($100\%$) $= 100 \times 3 = 300$. Hence, correct answer is (b).
By how much is 40% of 95 greater than 1/4 of 48?
95 का 40%, 48 के 1/4 से कितना अधिक है?
(A) (a) 24
(B) (b) 25
(C) (c) 26
(D) (d) 28
✅ Answer & Explanation
Sahi jawab: C) (c) 26Explanation: Method 1 (Ratio Conversion Method): • $40\% = \frac{2}{5} \implies \frac{2}{5} \times 95 = 2 \times 19 = 38$. • $\frac{1}{4} \text{ of } 48 = 12$. Difference $= 38 - 12 = 26$. Hence, correct option is (c) 26. Method 2 (Base Interchange Property Method): • Using property $a\% \text{ of } b = b\% \text{ of } a$: $40\% \text{ of } 95 = 95\% \text{ of } 40 = (100\% - 5\%) \text{ of } 40 = 40 - 2 = 38$. • $\frac{1}{4} \text{ of } 48 = 25\% \text{ of } 48 = 12$. Required difference $= 38 - 12 = 26$. Hence, correct answer is (c).
What is the ratio between X and Y if X is 45% of Y?
X और Y के बीच का अनुपात क्या है यदि X, Y का 45% है?
(A) (a) 9 : 20
(B) (b) 20 : 9
(C) (c) 9 : 11
(D) (d) 11 : 20
✅ Answer & Explanation
Sahi jawab: A) (a) 9 : 20Explanation: Method 1 (Ratio Method): $45\% = \frac{45}{100} = \frac{9}{20}$. Given $X = \frac{9}{20} Y \implies \frac{X}{Y} = \frac{9}{20} = 9 : 20$. Hence, correct option is (a) 9 : 20. Method 2 (100-Base Reference Method): Let $Y = 100$. Then $X = 45\% \text{ of } 100 = 45$. Ratio $X : Y = 45 : 100$. Dividing both numbers by 5: $X : Y = 9 : 20$. Hence, correct answer is (a).
If 24 pens out of 80 pens are blue and the rest are black, what is the percentage of black pens?
यदि 80 कलमों में से 24 नीली हैं और शेष काली हैं, तो काली कलमों का प्रतिशत क्या है?
(A) (a) 65%
(B) (b) 70%
(C) (c) 72%
(D) (d) 75%
✅ Answer & Explanation
Sahi jawab: B) (b) 70%Explanation: Method 1 (Ratio Method): Total pens $= 80$. Black pens $= 80 - 24 = 56$. Ratio of black pens to total $= \frac{56}{80} = \frac{7}{10}$. Since standard fraction $\frac{1}{10} = 10\%$, $\frac{7}{10} = 7 \times 10\% = 70\%$. Hence, correct option is (b) 70%. Method 2 (100-Base Complement Method): Calculate the percentage of blue pens first: Blue pens ratio $= \frac{24}{80} = \frac{3}{10} = 30\%$. Black pens percentage $= 100\% - 30\% = 70\%$. Hence, correct answer is (b).
In an office, the numbers of male and female employees are in the ratio of 7 : 9. What is the percentage of male employees in the office?
एक कार्यालय में पुरुष और महिला कर्मचारियों की संख्या 7 : 9 के अनुपात में है। कार्यालय में पुरुष कर्मचारियों का प्रतिशत क्या है?
(A) (a) 42.75%
(B) (b) 43.75%
(C) (c) 44.25%
(D) (d) 45.00%
✅ Answer & Explanation
Sahi jawab: B) (b) 43.75%Explanation: Method 1 (Fraction Ratio Method): Total units = Male (7 units) + Female (9 units) = 16 units. Fraction of males $= \frac{7}{16}$. Since standard unit fraction $\frac{1}{16} = 6.25\%$, $\frac{7}{16} = 7 \times 6.25\% = 43.75\%$. Hence, correct option is (b) 43.75%. Method 2 (100-Base Scaling Method): Total $= 7 + 9 = 16$ units. 16 units $= 100\% \implies 1 \text{ unit} = \frac{100}{16}\% = 6.25\%$. Males (7 units) $= 7 \times 6.25\% = 43.75\%$. Hence, correct answer is (b).
The cost price of a bicycle increased from ₹3,200 to ₹4,000. Find the increase percentage.
एक साइकिल का क्रय मूल्य ₹3,200 से बढ़कर ₹4,000 हो गया। प्रतिशत वृद्धि ज्ञात कीजिए।
(A) (a) 20%
(B) (b) 22.5%
(C) (c) 25%
(D) (d) 30%
✅ Answer & Explanation
Sahi jawab: C) (c) 25%Explanation: Method 1 (Ratio Method): Initial Price : Final Price $= 3200 : 4000 = 4 : 5$. Increment $= 5 - 4 = 1$ unit on base of 4 units. Percentage increase $= \frac{1}{4} = 25\%$. Hence, correct option is (c) 25%. Method 2 (100-Base Method): Absolute increase $= 4000 - 3200 = 800$. Base value $= 3200 = 100\%$. $1\% = 32$. Increase of ₹800 $= \frac{800}{32}\% = 25\%$. Hence, correct answer is (c).
The price of a watch drops from ₹400 to ₹280. What is the percentage decrease?
एक घड़ी का मूल्य ₹400 से घटकर ₹280 हो जाता है। प्रतिशत कमी क्या है?
(A) (a) 25%
(B) (b) 28%
(C) (c) 30%
(D) (d) 35%
✅ Answer & Explanation
Sahi jawab: C) (c) 30%Explanation: Method 1 (Ratio Method): Initial Price : New Price $= 400 : 280 = 10 : 7$. Decrease $= 10 - 7 = 3$ units on base of 10 units. Percentage decrease $= \frac{3}{10} = 30\%$. Hence, correct option is (c) 30%. Method 2 (100-Base Method): Initial value $= 400$. Divide both numbers by 4 to bring base to 100: Initial $= 100$, Final $= 70$. Reduction $= 100 - 70 = 30\%$. Hence, correct answer is (c).
Suresh's annual salary increased from ₹3,00,000 to ₹3,75,000. Find the percentage increase in his salary.
सुरेश का वार्षिक वेतन ₹3,00,000 से बढ़कर ₹3,75,000 हो गया। उसके वेतन में प्रतिशत वृद्धि ज्ञात कीजिए।
(A) (a) 20%
(B) (b) 25%
(C) (c) 30%
(D) (d) 35%
✅ Answer & Explanation
Sahi jawab: B) (b) 25%Explanation: Method 1 (Ratio Method): Initial Salary : Increased Salary $= 300000 : 375000 = 4 : 5$. Increment $= 5 - 4 = 1$ unit on base of 4 units. Percentage increase $= \frac{1}{4} = 25\%$. Hence, correct option is (b) 25%. Method 2 (100-Base Method): Initial Salary $= 3,00,000 = 100\%$. Net increase $= 75,000$. Dividing both by 3000: Base $= 100$, Increment $= \frac{75000}{3000} = 25\%$. Hence, correct answer is (b).
Aman's income decreased from ₹65,000 to ₹55,900. Find the percentage decrease in his income.
अमन की आय ₹65,000 से घटकर ₹55,900 हो गई। उसकी आय में प्रतिशत कमी ज्ञात कीजिए।
(A) (a) 12%
(B) (b) 13%
(C) (c) 14%
(D) (d) 15%
✅ Answer & Explanation
Sahi jawab: C) (c) 14%Explanation: Method 1 (Ratio Method): Decrease in income $= 65000 - 55900 = 9100$. Fraction of decrease $= \frac{9100}{65000} = \frac{91}{650} = \frac{7}{50}$. Since standard fraction $\frac{1}{50} = 2\%$, $\frac{7}{50} = 7 \times 2\% = 14\%$. Hence, correct option is (c) 14%. Method 2 (10% and 1% Base Splitting Method): Base income $= 65000 = 100\%$. $10\% = 6500$. Remaining reduction $= 9100 - 6500 = 2600$. Since $1\% = 650$, $2600 = 4 \times 650 \implies 4\%$. Total decrease $= 10\% + 4\% = 14\%$. Hence, correct answer is (c).
The population of a town increased from 40,000 to 47,200 in a year. What is the percentage increase?
एक वर्ष में एक कस्बे की जनसंख्या 40,000 से बढ़कर 47,200 हो गई। प्रतिशत वृद्धि क्या है?
(A) (a) 16%
(B) (b) 17%
(C) (c) 18%
(D) (d) 19%
✅ Answer & Explanation
Sahi jawab: C) (c) 18%Explanation: Method 1 (Ratio Method): Initial : New $= 40000 : 47200 = 50 : 59$. Increase $= 59 - 50 = 9$ units on base of 50 units. Percentage increase $= \frac{9}{50} = 9 \times 2\% = 18\%$. Hence, correct option is (c) 18%. Method 2 (100-Base Method): Divide both numbers by 400 to establish base 100: Initial Base $= 100$, New Base $= 118$. Increment $= 118 - 100 = 18\%$. Hence, correct answer is (c).
Last year, Vikrant's monthly salary was ₹45,000 and this year his monthly salary is ₹51,750. What is the percentage increase in Vikrant's monthly salary this year over his monthly salary last year?
पिछले वर्ष विक्रांत का मासिक वेतन ₹45,000 था और इस वर्ष उसका मासिक वेतन ₹51,750 है। पिछले वर्ष के मासिक वेतन की तुलना में इस वर्ष विक्रांत के मासिक वेतन में कितने प्रतिशत की वृद्धि हुई है?
(A) (a) 12%
(B) (b) 14%
(C) (c) 15%
(D) (d) 18%
✅ Answer & Explanation
Sahi jawab: C) (c) 15%Explanation: Method 1 (Ratio Method): Initial Salary : New Salary $= 45000 : 51750 = 20 : 23$. Increase $= 23 - 20 = 3$ units on base of 20 units. Percentage increase $= \frac{3}{20} \times 100\% = 15\%$. Hence, correct option is (c) 15%. Method 2 (10% and 1% Base Splitting Method): Net increase $= 51750 - 45000 = 6750$. Base salary $= 45000 = 100\%$. $10\% = 4500$, $5\% = 2250$. $4500 + 2250 = 6750 \implies 10\% + 5\% = 15\%$. Hence, correct answer is (c).
Ananya invests ₹1,80,000, which is 25% of her annual income, in mutual funds. What is her monthly income (in ₹)?
अनन्या ₹1,80,000 का निवेश करती है, जो उसकी वार्षिक आय का 25% है, म्यूचुअल फंड में। उसकी मासिक आय (₹ में) क्या है?
(A) (a) 50000
(B) (b) 60000
(C) (c) 55000
(D) (d) 65000
✅ Answer & Explanation
Sahi jawab: B) (b) 60000Explanation: Method 1 (Ratio Method): $25\% = \frac{1}{4}$. 1 unit of Annual Income $= 180000$. Total Annual Income (4 units) $= 4 \times 180000 = 720000$. Monthly Income $= \frac{720000}{12} = 60000$. Hence, correct option is (b) 60000. Method 2 (100-Base Method): $25\% \text{ of Annual Income} = 180000$. Annual Income ($100\%$) $= 180000 \times 4 = 720000$. Monthly Income $= \frac{720000}{12} = 60000$. Hence, correct answer is (b).
An interval of 3 hours 20 minutes is wrongly estimated by 3 hours 27 minutes. The error percentage is:
3 घंटे 20 मिनट के अंतराल का गलत अनुमान 3 घंटे 27 मिनट लगाया जाता है। त्रुटि प्रतिशत क्या है?
(A) (a) 3.2%
(B) (b) 3.5%
(C) (c) 3.8%
(D) (d) 4.0%
✅ Answer & Explanation
Sahi jawab: B) (b) 3.5%Explanation: Method 1 (Ratio Method): True value $= 3 \times 60 + 20 = 200 \text{ minutes}$. Estimated value $= 3 \times 60 + 27 = 207 \text{ minutes}$. Error $= 207 - 200 = 7 \text{ minutes}$. Percentage $= \frac{7}{200} \times 100\% = 3.5\%$. Hence, correct option is (b) 3.5%. Method 2 (100-Base Step Method): Base value $= 200 \text{ minutes} = 100\%$. $1 \text{ minute} = 0.5\%$. Error $= 7 \text{ minutes} = 7 \times 0.5\% = 3.5\%$. Hence, correct answer is (b).
The population of a city was 8000000 in 2021. The population grows 5% annually. The population in 2023 is:
2021 में एक शहर की जनसंख्या 80,00,000 थी। जनसंख्या में प्रतिवर्ष 5% की वृद्धि होती है। 2023 में जनसंख्या कितनी होगी?
(A) (a) 8820000
(B) (b) 8800000
(C) (c) 8720000
(D) (d) 8920000
✅ Answer & Explanation
Sahi jawab: A) (a) 8820000Explanation: Method 1 (Ratio Method): $5\% = \frac{1}{20}$. Factor $= 1 + \frac{1}{20} = \frac{21}{20}$. Population in 2023 $= 8000000 \times \frac{21}{20} \times \frac{21}{20} = 20000 \times 441 = 8820000$. Hence, correct option is (a) 8820000. Method 2 (Successive Percentage Base Method): Effective increase over 2 years $= 5 + 5 + \frac{25}{100} = 10.25\%$. Population in 2023 $= 8000000 + (10.25\% \text{ of } 8000000) = 8000000 + 820000 = 8820000$. Hence, correct answer is (a).
After an increase of 8% in salary, an employee receives ₹6,480. What was the initial salary?
वेतन में 8% की वृद्धि के बाद, एक कर्मचारी को ₹6,480 मिलते हैं। प्रारंभिक वेतन क्या था?
(A) (a) ₹5,800
(B) (b) ₹6,000
(C) (c) ₹6,100
(D) (d) ₹5,900
✅ Answer & Explanation
Sahi jawab: B) (b) ₹6,000Explanation: Method 1 (Ratio Method): $8\% = \frac{2}{25}$. Initial : Increased $= 25 : 27$. 27 units $= 6480 \implies 1 \text{ unit} = 240$. Initial salary = 25 units $= 25 \times 240 = 6000$. Hence, correct option is (b) ₹6,000. Method 2 (100-Base Method): $108\% = 6480 \implies 1\% = 60$. Original salary ($100\%$) $= 60 \times 100 = 6000$. Hence, correct answer is (b).
P gives 2/5 of the chocolates he has to Q. If now P has m% of the chocolates with Q, then find the value of m.
P अपने पास मौजूद चॉकलेटों का 2/5 भाग Q को देता है। यदि अब P के पास Q के पास मौजूद चॉकलेटों का m% है, तो m का मान ज्ञात कीजिए।
(A) (a) 120
(B) (b) 125
(C) (c) 150
(D) (d) 160
✅ Answer & Explanation
Sahi jawab: C) (c) 150Explanation: Method 1 (Ratio Method): Let initial total chocolates with P = 5 units. Given to Q = 2 units. Remaining with P = 3 units. P's chocolates as a percentage of Q's chocolates $= \frac{3}{2} \times 100\% = 150\%$. Therefore, $m = 150$. Hence, correct option is (c) 150. Method 2 (100-Base Method): Assume P initially has 500 chocolates. Given to Q $= 200$. Remaining with P $= 300$. $300 = \frac{m}{100} \times 200 \implies 2m = 300 \implies m = 150$. Hence, correct answer is (c).
If 20% of Aman's income is equal to 30% of Bhuvan's income, then 40% of Aman's income is equal to what percentage of Bhuvan's income?
यदि अमन की आय का 20%, भुवन की आय के 30% के बराबर है, तो अमन की आय का 40%, भुवन की आय के कितने प्रतिशत के बराबर है?
(A) (a) 50%
(B) (b) 60%
(C) (c) 65%
(D) (d) 75%
✅ Answer & Explanation
Sahi jawab: B) (b) 60%Explanation: Method 1 (Ratio Method): $20\% \times \text{Aman} = 30\% \times \text{Bhuvan} \implies \frac{\text{Aman}}{\text{Bhuvan}} = \frac{3}{2}$. $40\% \text{ of Aman} = 0.40 \times 3 = 1.2$ units. Percentage with respect to Bhuvan (2 units) $= \frac{1.2}{2} \times 100\% = 60\%$. Hence, correct option is (b) 60%. Method 2 (Direct Proportionality Method): $20\% \text{ of Aman} = 30\% \text{ of Bhuvan}$. Multiplying both sides by 2: $40\% \text{ of Aman} = 60\% \text{ of Bhuvan}$. Hence, correct answer is (b).
A number increased by 25% gives 350. Find the number.
एक संख्या में 25% की वृद्धि करने पर 350 प्राप्त होता है। संख्या ज्ञात कीजिए।
(A) (a) 260
(B) (b) 275
(C) (c) 280
(D) (d) 300
✅ Answer & Explanation
Sahi jawab: C) (c) 280Explanation: Method 1 (Ratio Method): $25\% = \frac{1}{4}$. Original number = 4 units, Increased number = 5 units. 5 units $= 350 \implies 1 \text{ unit} = 70$. Original number = 4 units $= 4 \times 70 = 280$. Hence, correct option is (c) 280. Method 2 (100-Base Method): $125\% = 350 \implies 25\% = 70$. Original number ($100\%$) $= 70 \times 4 = 280$. Hence, correct answer is (c).
When a number is increased by 15, it becomes 125% of itself. The number is:
जब किसी संख्या में 15 की वृद्धि की जाती है, तो वह स्वयं का 125% हो जाती है। वह संख्या क्या है?
(A) (a) 45
(B) (b) 60
(C) (c) 75
(D) (d) 90
✅ Answer & Explanation
Sahi jawab: B) (b) 60Explanation: Method 1 (Ratio Method): $125\% = \frac{5}{4}$. Increase $= 5 - 4 = 1$ unit. 1 unit $= 15$. Original number = 4 units $= 4 \times 15 = 60$. Hence, correct option is (b) 60. Method 2 (100-Base Method): Percentage increase $= 125\% - 100\% = 25\%$. $25\% = 15$. $100\% = 15 \times 4 = 60$. Hence, correct answer is (b).
When 18 is subtracted from a number, it reduces to its 70%. What is 45% of that number?
जब किसी संख्या में से 18 घटाया जाता है, तो वह घटकर अपने 70% पर आ जाती है। उस संख्या का 45% क्या है?
(A) (a) 18
(B) (b) 24
(C) (c) 25
(D) (d) 27
✅ Answer & Explanation
Sahi jawab: D) (d) 27Explanation: Method 1 (Ratio Method): $70\% = \frac{7}{10}$. Reduction $= 10 - 7 = 3$ units. 3 units $= 18 \implies 1 \text{ unit} = 6$. Original number = 10 units $= 10 \times 6 = 60$. $45\% \text{ of } 60 = \frac{9}{20} \times 60 = 27$. Hence, correct option is (d) 27. Method 2 (100-Base Method): Reduction $= 100\% - 70\% = 30\%$. Given: $30\% = 18 \implies 10\% = 6$. Number $= 60$. $45\% \text{ of } 60 = 0.45 \times 60 = 27$. Hence, correct answer is (d).
If 45 is subtracted from 45% of a number, the remainder is 45. What is the number?
यदि किसी संख्या के 45% में से 45 घटाया जाता है, तो शेषफल 45 प्राप्त होता है। वह संख्या क्या है?
(A) (a) 150
(B) (b) 200
(C) (c) 250
(D) (d) 300
✅ Answer & Explanation
Sahi jawab: B) (b) 200Explanation: Method 1 (Ratio Method): $45\% = \frac{9}{20}$. $\frac{9}{20} \text{ of number} - 45 = 45 \implies \frac{9}{20} \text{ of number} = 90$. 9 units $= 90 \implies 1 \text{ unit} = 10$. Total number (20 units) $= 20 \times 10 = 200$. Hence, correct option is (b) 200. Method 2 (100-Base Method): $45\% - 45 = 45 \implies 45\% = 90$. $1\% = 2$. Original number ($100\%$) $= 2 \times 100 = 200$. Hence, correct answer is (b).
Two numbers are respectively 30% less and 40% more than a third number. What is the ratio of the two numbers?
दो संख्याएँ एक तीसरी संख्या से क्रमशः 30% कम और 40% अधिक हैं। दोनों संख्याओं का अनुपात क्या है?
(A) (a) 1 : 2
(B) (b) 2 : 3
(C) (c) 3 : 4
(D) (d) 4 : 5
✅ Answer & Explanation
Sahi jawab: A) (a) 1 : 2Explanation: Method 1 (100-Base Reference Method): Let third number be 100. First number $= 100 - 30 = 70$. Second number $= 100 + 40 = 140$. Ratio $= 70 : 140 = 1 : 2$. Hence, correct option is (a) 1 : 2. Method 2 (Ratio Method): Let third number = 10 units. First number $= 7$ units, Second number $= 14$ units. Ratio $= 7 : 14 = 1 : 2$. Hence, correct answer is (a).
Two numbers are respectively 44% and 20% less than a third number. The first number is what percentage of the second number?
दो संख्याएँ एक तीसरी संख्या से क्रमशः 44% और 20% कम हैं। पहली संख्या दूसरी संख्या का कितना प्रतिशत है?
(A) (a) 65%
(B) (b) 70%
(C) (c) 72%
(D) (d) 75%
✅ Answer & Explanation
Sahi jawab: B) (b) 70%Explanation: Method 1 (100-Base Method): Let third number be 100. First number $= 100 - 44 = 56$. Second number $= 100 - 20 = 80$. Percentage $= \frac{56}{80} \times 100\% = \frac{7}{10} \times 100\% = 70\%$. Hence, correct option is (b) 70%. Method 2 (Ratio Method): First : Second $= 56 : 80 = 7 : 10$. Since $\frac{1}{10} = 10\%$, $\frac{7}{10} = 70\%$. Hence, correct answer is (b).
Last year, Sumit's monthly salary was ₹40,000 and this year his monthly salary is ₹46,400. What is the percentage increase in Sumit's monthly salary this year over his monthly salary last year?
पिछले वर्ष सुमित का मासिक वेतन ₹40,000 था और इस वर्ष उसका मासिक वेतन ₹46,400 है। पिछले वर्ष के मासिक वेतन की तुलना में इस वर्ष सुमित के मासिक वेतन में कितने प्रतिशत की वृद्धि हुई है?
(A) (a) 14%
(B) (b) 16%
(C) (c) 15%
(D) (d) 18%
✅ Answer & Explanation
Sahi jawab: B) (b) 16%Explanation: Method 1 (Ratio Method): Initial Salary : New Salary $= 40000 : 46400 = 25 : 29$. Increase $= 29 - 25 = 4$ units on base of 25 units. Percentage increase $= \frac{4}{25} \times 100\% = 16\%$. Hence, correct option is (b) 16%. Method 2 (10% and 1% Base Splitting Method): Net increase $= 46400 - 40000 = 6400$. Base $= 40000 = 100\%$. $10\% = 4000$, $6\% = 2400$. Total increase $= 10\% + 6\% = 16\%$. Hence, correct answer is (b).
Pooja invests ₹1,68,000, which is 35% of her annual income, in mutual funds. What is her monthly income (in ₹)?
पूजा ₹1,68,000 का निवेश करती है, जो उसकी वार्षिक आय का 35% है, म्यूचुअल फंड में। उसकी मासिक आय (₹ में) क्या है?
(A) (a) 38000
(B) (b) 42000
(C) (c) 40000
(D) (d) 45000
✅ Answer & Explanation
Sahi jawab: C) (c) 40000Explanation: Method 1 (Ratio Method): $35\% = \frac{7}{20}$. 7 units $= 168000 \implies 1 \text{ unit} = 24000$. Annual Income (20 units) $= 20 \times 24000 = 480000$. Monthly Income $= \frac{480000}{12} = 40000$. Hence, correct option is (c) 40000. Method 2 (100-Base Method): $35\% = 168000 \implies 1\% = 4800$. Annual Income ($100\%$) $= 480000$. Monthly Income $= \frac{480000}{12} = 40000$. Hence, correct answer is (c).
An interval of 2 hours 40 minutes is wrongly estimated by 2 hours 46.4 minutes. The error percentage is:
2 घंटे 40 मिनट के अंतराल का गलत अनुमान 2 घंटे 46.4 मिनट लगाया जाता है। त्रुटि प्रतिशत क्या है?
(A) (a) 3.5%
(B) (b) 4.2%
(C) (c) 4.0%
(D) (d) 4.5%
✅ Answer & Explanation
Sahi jawab: C) (c) 4.0%Explanation: Method 1 (Ratio Method): True value $= 160 \text{ minutes}$, Estimated $= 166.4 \text{ minutes}$. Error $= 6.4 \text{ minutes}$. Ratio $= \frac{6.4}{160} = \frac{1}{25} = 4\%$. Hence, correct option is (c) 4.0%. Method 2 (100-Base Step Method): Base $= 160 \text{ minutes} = 100\% \implies 1\% = 1.6 \text{ minutes}$. Error percentage $= \frac{6.4}{1.6} = 4\%$. Hence, correct answer is (c).