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A school conducted a scholarship test where 60% of the students passed in English, 70% passed in Math, and 45% passed in both. What is the percentage of students who passed in at least one subject?
एक विद्यालय ने एक छात्रवृत्ति परीक्षा आयोजित की जिसमें 60% छात्र अंग्रेजी में, 70% गणित में और 45% दोनों में उत्तीर्ण हुए। कम से कम एक विषय में उत्तीर्ण होने वाले छात्रों का प्रतिशत क्या है?
(A) (a) 90%
(B) (b) 75%
(C) (c) 85%
(D) (d) 80%
✅ Answer & Explanation
Sahi jawab: C) (c) 85%Explanation: Method 1 (Set Theory Formula): At least one subject me pass hone wale students: $P(E \cup M) = P(E) + P(M) - P(E \cap M)$ $= 60\% + 70\% - 45\% = 130\% - 45\% = 85\%$. Atah sahi vikalp (c) 85% hai. Method 2 (Venn Diagram Method): Only English me pass = $60\% - 45\% = 15\%$. Only Math me pass = $70\% - 45\% = 25\%$. Both English & Math = $45\%$. At least one subject = $15\% + 25\% + 45\% = 85\%$. Atah sahi uttar (c) hai.
In a school, the total no. of students who play tennis and cricket both is 180. In that school 70% of the total students play tennis and 60% of the total students play cricket. If the percentage of the students who do not play any game is 25% of the percentage of the students who play cricket, then find the total number of students?
एक विद्यालय में टेनिस और क्रिकेट दोनों खेलने वाले विद्यार्थियों की कुल संख्या 180 है। उस विद्यालय में कुल विद्यार्थियों में से 70% टेनिस खेलते हैं और 60% क्रिकेट खेलते हैं। यदि कोई भी खेल न खेलने वाले विद्यार्थियों का प्रतिशत, क्रिकेट खेलने वाले विद्यार्थियों के प्रतिशत का 25% है, तो विद्यार्थियों की कुल संख्या ज्ञात कीजिए।
(A) (a) 500
(B) (b) 600
(C) (c) 400
(D) (d) 480
✅ Answer & Explanation
Sahi jawab: C) (c) 400Explanation: Method 1 (100-Base Method): Total students = $100\%$. Tennis ($T$) = $70\%$. Cricket ($C$) = $60\%$. Neither game = $25\% \text{ of } 60\% = \frac{1}{4} \times 60\% = 15\%$. At least one game ($T \cup C$) = $100\% - 15\% = 85\%$. We know: $n(T \cup C) = n(T) + n(C) - n(T \cap C)$. $85\% = 70\% + 60\% - n(T \cap C)$ $85\% = 130\% - n(T \cap C) \implies n(T \cap C) = 130\% - 85\% = 45\%$. Given: $45\% = 180$. $1\% = \frac{180}{45} = 4$. Total number of students ($100\%$) = $4 \times 100 = 400$. Atah sahi vikalp (c) 400 hai. Method 2 (Ratio Method): Both sports percentage = $45\% = \frac{9}{20}$. Given: $9\text{ units} = 180 \implies 1\text{ unit} = 20$. Total students = $20\text{ units} = 20 \times 20 = 400$. Atah sahi uttar (c) hai.
In a survey conducted at a university, it was found that 55% of the students like Mathematics, 45% like Physics, and 30% like both Mathematics and Physics. Among the remaining students, 25% prefer Computer Science, while the rest have no preference. If the total number of students surveyed is 800, how many students had no preference for any of the three subjects?
एक विश्वविद्यालय में किए गए एक सर्वेक्षण में पाया गया कि 55% छात्र गणित पसंद करते हैं, 45% भौतिकी पसंद करते हैं, और 30% गणित और भौतिकी दोनों पसंद करते हैं। शेष छात्रों में से 25% कंप्यूटर विज्ञान पसंद करते हैं, जबकि शेष की कोई प्राथमिकता नहीं है। यदि सर्वेक्षण में शामिल कुल छात्रों की संख्या 800 है, तो कितने छात्रों की तीनों विषयों में से किसी के लिए भी कोई प्राथमिकता नहीं थी?
(A) (a) 160
(B) (b) 200
(C) (c) 220
(D) (d) 180
✅ Answer & Explanation
Sahi jawab: D) (d) 180Explanation: Method 1 (Percentage Multiplier Method): Students liking Math or Physics: $n(M \cup P) = 55\% + 45\% - 30\% = 70\%$. Remaining students = $100\% - 70\% = 30\%$. Among the remaining, $25\%$ prefer Computer Science, so the rest with no preference: $= (100\% - 25\%) \text{ of } 30\% = 75\% \text{ of } 30\% = \frac{3}{4} \times 30\% = 22.5\%$. Total students with no preference = $22.5\% \text{ of } 800 = \frac{22.5}{100} \times 800 = 22.5 \times 8 = 180$. Atah sahi vikalp (d) 180 hai. Method 2 (Direct Count Method): Total students = $800$. Remaining count = $30\% \text{ of } 800 = 240$. Computer Science count = $25\% \text{ of } 240 = 60$. No preference count = $240 - 60 = 180$. Atah sahi uttar (d) hai.
In a village of 800 people, 60% speaks Hindi, 20% speak English only. If the number of people who did not speak any language is equal to the number of people who speak both languages, then find the number of people who speak both languages.
800 लोगों के एक गांव में, 60% हिंदी बोलते हैं, 20% केवल अंग्रेजी बोलते हैं। यदि कोई भी भाषा न बोलने वाले लोगों की संख्या दोनों भाषाएं बोलने वाले लोगों की संख्या के बराबर है, तो दोनों भाषाएं बोलने वाले लोगों की संख्या ज्ञात कीजिए।
(A) (a) 320
(B) (b) 160
(C) (c) 200
(D) (d) 180
✅ Answer & Explanation
Sahi jawab: B) (b) 160Explanation: Method 1 (100-Base Method): Total people = $100\% = 800$. Hindi ($H$) = $60\%$. Only English = $20\%$. Let both languages = $x\%$. Then neither language = $x\%$. Total = (People who speak Hindi) + (Only English) + (Neither language) $100\% = 60\% + 20\% + x\%$ $100\% = 80\% + x\% \implies x\% = 20\%$. Number of people who speak both languages = $20\% \text{ of } 800 = \frac{20}{100} \times 800 = 160$. Atah sahi vikalp (b) 160 hai. Method 2 (Count Equation Method): Total = $800$. Hindi speaking = $60\% \text{ of } 800 = 480$. Only English = $20\% \text{ of } 800 = 160$. Let both = $B$. Then neither = $B$. Total = (Hindi) + (Only English) + (Neither) $800 = 480 + 160 + B \implies 800 = 640 + B \implies B = 160$. Atah sahi uttar (b) hai.
A company conducted a survey for THE HINDU and TIMES OF INDIA. By survey it is known that the number of people who like both is equal to the people who did not like anyone. 630 people like only TIMES OF INDIA and 48% like TIMES OF INDIA. If there are a total of 1750 people in the survey, then find the percentage of people who like only THE HINDU.
एक कंपनी ने द हिंदू और टाइम्स ऑफ इंडिया के लिए एक सर्वेक्षण किया। सर्वेक्षण से यह ज्ञात हुआ कि दोनों को पसंद करने वाले लोगों की संख्या उन लोगों के बराबर है जो किसी को भी पसंद नहीं करते हैं। 630 लोग केवल टाइम्स ऑफ इंडिया पसंद करते हैं और 48% टाइम्स ऑफ इंडिया पसंद करते हैं। यदि सर्वेक्षण में कुल 1750 लोग हैं, तो केवल द हिंदू पसंद करने वाले लोगों का प्रतिशत ज्ञात कीजिए।
(A) (a) 40%
(B) (b) 25%
(C) (c) 30%
(D) (d) 60%
✅ Answer & Explanation
Sahi jawab: A) (a) 40%Explanation: Method 1 (Absolute Count Method): Total people surveyed = $1750$. People who like Times of India (TOI) = $48\% \text{ of } 1750 = 0.48 \times 1750 = 840$. Only TOI = $630$. People who like both = $\text{TOI} - \text{Only TOI} = 840 - 630 = 210$. Given: People who did not like either (Neither) = Both = $210$. Now, Total = (Only Hindu) + (TOI) + (Neither) $1750 = \text{Only Hindu} + 840 + 210$ $1750 = \text{Only Hindu} + 1050 \implies \text{Only Hindu} = 1750 - 1050 = 700$. Percentage of people who like only The Hindu = $\frac{700}{1750} \times 100\% = \frac{2}{5} \times 100\% = 40\%$. Atah sahi vikalp (a) 40% hai. Method 2 (100-Base Method): Only TOI percentage = $\frac{630}{1750} \times 100\% = 36\%$. Both percentage = $48\% - 36\% = 12\%$. Neither percentage = Both percentage = $12\%$. Total ($100\%$) = (Only Hindu) + (TOI) + (Neither) $100\% = \text{Only Hindu} + 48\% + 12\% \implies \text{Only Hindu} = 100\% - 60\% = 40\%$. Atah sahi uttar (a) hai.
In an examination, 50% students passed in physics, 37.5% students passed in chemistry, and 12.5% students passed in both. If in that exam the number of girls is equal to the number of failed students, and 25% of the failed students are girls, which is 20, then find what percent of boys failed?
एक परीक्षा में 50% छात्र भौतिकी में, 37.5% छात्र रसायन विज्ञान में और 12.5% छात्र दोनों में उत्तीर्ण हुए। यदि उस परीक्षा में लड़कियों की संख्या अनुत्तीर्ण छात्रों की संख्या के बराबर है और अनुत्तीर्ण छात्रों में से 25% लड़कियां हैं, जो कि 20 हैं, तो अनुत्तीर्ण होने वाले लड़कों का प्रतिशत ज्ञात कीजिए?
(A) (a) 50%
(B) (b) 60%
(C) (c) 25%
(D) (d) 66.67%
✅ Answer & Explanation
Sahi jawab: C) (c) 25%Explanation: Method 1 (Venn Diagram & Step Breakdown): Passed in at least one subject: $P(P \cup C) = 50\% + 37.5\% - 12.5\% = 75\%$. Total failed students (failed in both) = $100\% - 75\% = 25\%$. Given: $25\%$ of failed students are girls, which is 20: $0.25 \times \text{Total Failed} = 20 \implies \text{Total Failed} = 80$. Number of failed boys = $80 - 20 = 60$. Total students in the exam: $25\% \text{ of Total Students} = 80 \implies \text{Total Students} = 80 \times 4 = 320$. Total girls = Total failed students = $80$. Total boys = $\text{Total Students} - \text{Total Girls} = 320 - 80 = 240$. Percent of boys who failed = $\frac{\text{Failed Boys}}{\text{Total Boys}} \times 100\% = \frac{60}{240} \times 100\% = 25\%$. Atah sahi vikalp (c) 25% hai. Method 2 (Ratio Method): Failed boys = 60, Total boys = 240. Ratio = $\frac{60}{240} = \frac{1}{4} = 25\%$. Atah sahi uttar (c) hai.
In a college exam, 43 passed in accounts, 42 passed in digital marketing and 40 passed in social science. In all the three exams 10 got passing marks. 22 passed accounts and digital marketing, 23 passed in accounts and social science, 16 passed in digital marketing and social science. Find how much percentage of the students passed only in two subjects to students passed only in one subject.
एक कॉलेज परीक्षा में, 43 छात्र अकाउंट्स में, 42 डिजिटल मार्केटिंग में और 40 सोशल साइंस में उत्तीर्ण हुए। तीनों परीक्षाओं में 10 को उत्तीर्ण अंक प्राप्त हुए। 22 अकाउंट्स और डिजिटल मार्केटिंग में, 23 अकाउंट्स और सोशल साइंस में, 16 डिजिटल मार्केटिंग और सोशल साइंस में उत्तीर्ण हुए। ज्ञात कीजिए कि केवल दो विषयों में उत्तीर्ण होने वाले छात्रों की संख्या, केवल एक विषय में उत्तीर्ण होने वाले छात्रों की संख्या का कितना प्रतिशत है?
(A) (a) 93.99%
(B) (b) 9.3%
(C) (c) 11.11%
(D) (d) 95%
✅ Answer & Explanation
Sahi jawab: A) (a) 93.99%Explanation: Method 1 (Venn Diagram Method): Given: - All three subjects = 10 - Students passed in exactly two subjects: - Accounts & Digital Marketing only = 22 - 10 = 12 - Accounts & Social Science only = 23 - 10 = 13 - Digital Marketing & Social Science only = 16 - 10 = 6 - Total passed in exactly two subjects = 12 + 13 + 6 = 31 - Students passed in exactly one subject: - Accounts only = 43 - (12 + 13 + 10) = 43 - 35 = 8 - Digital Marketing only = 42 - (12 + 6 + 10) = 42 - 28 = 14 - Social Science only = 40 - (13 + 6 + 10) = 40 - 29 = 11 - Total passed in exactly one subject = 8 + 14 + 11 = 33 Required percentage = (31 / 33) * 100% ≈ 93.939% ≈ 93.99%. Atah sahi vikalp (a) 93.99% hai. Method 2 (Formula Method): Sum of double intersections = 22 + 23 + 16 = 61. Number of students in exactly two subjects = 61 - 3 * 10 = 31. Sum of single subjects = 43 + 42 + 40 = 125. Number of students in exactly one subject = 125 - 2 * 61 + 3 * 10 = 125 - 122 + 30 = 33. Required percentage = (31 / 33) * 100% ≈ 93.99%. Atah sahi uttar (a) hai.
In an examination, 53% of students passed in Mathematics, 61% passed in Physics, and 60% passed in Chemistry. In pair combinations, 24% passed in Math & Physics, 35% in Physics & Chemistry, and 27% in Math & Chemistry. If 5% of students passed in none of the subjects, find the ratio of the percentage of students passing in Math & Chemistry but not Physics to those passing in Physics & Chemistry but not Math.
एक परीक्षा में 53% विद्यार्थी गणित में, 61% भौतिकी में और 60% रसायन विज्ञान में उत्तीर्ण हुए। युग्मों में, 24% गणित और भौतिकी में, 35% भौतिकी और रसायन में तथा 27% गणित और रसायन में उत्तीर्ण हुए। यदि 5% विद्यार्थी किसी भी विषय में उत्तीर्ण नहीं हुए, तो गणित और रसायन में उत्तीर्ण लेकिन भौतिकी में नहीं, का भौतिकी और रसायन में उत्तीर्ण लेकिन गणित में नहीं होने वाले विद्यार्थियों से अनुपात क्या है?
(A) (a) 7 : 5
(B) (b) 5 : 7
(C) (c) 4 : 5
(D) (d) 5 : 4
✅ Answer & Explanation
Sahi jawab: B) (b) 5 : 7Explanation: Method 1 (Set Theory Union Formula): Students passing in at least one subject = 100% - 5% = 95%. Let x% be the percentage passing in all three subjects. Using the three-set principle: 95 = (53 + 61 + 60) - (24 + 35 + 27) + x 95 = 174 - 86 + x 95 = 88 + x ==> x = 7%. Now find the exclusive two-subject regions: - Passing Math & Chemistry but not Physics = (Math ∩ Chemistry) - (All three) = 27% - 7% = 20%. - Passing Physics & Chemistry but not Math = (Physics ∩ Chemistry) - (All three) = 35% - 7% = 28%. Required Ratio = 20% : 28% = 5 : 7. Atah sahi vikalp (b) 5 : 7 hai. Method 2 (Region Allocation): Directly subtracting the central triple intersection x = 7%: Only (M ∩ C) = 27 - 7 = 20%. Only (P ∩ C) = 35 - 7 = 28%. Ratio = 20 : 28 = 5 : 7. Atah sahi uttar (b) hai.
In a class of 50 students, 20 play hockey, 15 play cricket, and 11 play football. Exactly 7 play both hockey and cricket, 4 play cricket and football, and 5 play hockey and football. If 18 students do not play any of the three sports, find the ratio of students who play all three sports to those who play exactly two of these sports.
50 विद्यार्थियों की एक कक्षा में, 20 हॉकी खेलते हैं, 15 क्रिकेट खेलते हैं और 11 फुटबॉल खेलते हैं। 7 विद्यार्थी हॉकी और क्रिकेट दोनों खेलते हैं, 4 क्रिकेट और फुटबॉल खेलते हैं, तथा 5 हॉकी और फुटबॉल खेलते हैं। यदि 18 विद्यार्थी इनमें से कोई भी खेल नहीं खेलते हैं, तो तीनों खेल खेलने वाले विद्यार्थियों का केवल दो खेल खेलने वाले विद्यार्थियों से अनुपात ज्ञात कीजिए।
(A) (a) 1 : 3
(B) (b) 1 : 7
(C) (c) 1 : 5
(D) (d) 4 : 3
✅ Answer & Explanation
Sahi jawab: C) (c) 1 : 5Explanation: Method 1 (Inclusion-Exclusion Principle): Students playing at least one game = 50 - 18 = 32. Let k denote the number of students playing all three games. Using the union formula: 32 = (20 + 15 + 11) - (7 + 4 + 5) + k 32 = 46 - 16 + k 32 = 30 + k ==> k = 2. Students playing exactly two sports: = (7 - k) + (4 - k) + (5 - k) = (7 - 2) + (4 - 2) + (5 - 2) = 5 + 2 + 3 = 10. Required Ratio = (All three) : (Exactly two) = 2 : 10 = 1 : 5. Atah sahi vikalp (c) 1 : 5 hai. Method 2 (Venn Diagram Regions): Triple overlap = 2. Hockey & Cricket only = 7 - 2 = 5. Cricket & Football only = 4 - 2 = 2. Hockey & Football only = 5 - 2 = 3. Total in exactly two = 5 + 2 + 3 = 10. Ratio = 2 : 10 = 1 : 5. Atah sahi uttar (c) hai.
A company pays 13% commission on overall sales. Alternatively, a salesman can opt for a fixed monthly salary of ₹4,700 along with a 7% commission on sales exceeding ₹12,000. Under the second option, his earnings are ₹620 higher. Find the total sales made by the salesman.
एक कंपनी कुल बिक्री पर 13% कमीशन देती है। वैकल्पिक रूप से, विक्रेता ₹4,700 का निश्चित वेतन और ₹12,000 से अधिक की बिक्री पर 7% कमीशन प्राप्त कर सकता है। दूसरे विकल्प के तहत उसे ₹620 अधिक मिलते हैं। विक्रेता द्वारा की गई कुल बिक्री ज्ञात कीजिए।
(A) (a) ₹50,000
(B) (b) ₹52,000
(C) (c) ₹57,000
(D) (d) ₹54,000
✅ Answer & Explanation
Sahi jawab: D) (d) ₹54,000Explanation: Method 1 (Equation Method): Let total sales be S. Commission under Option 1 = 0.13 * S. Earnings under Option 2 = 4700 + 0.07 * (S - 12000) = 4700 + 0.07 * S - 840 = 3860 + 0.07 * S. Given: (3860 + 0.07 * S) - 0.13 * S = 620 3860 - 0.06 * S = 620 0.06 * S = 3860 - 620 = 3240 S = 3240 / 0.06 = ₹54,000. Atah sahi vikalp (d) ₹54,000 hai. Method 2 (Shift Method): If the 7% rate applied from zero sales, the fixed amount would reduce by 7% of 12000 = ₹840, giving 4700 - 840 = ₹3860. The net difference between 13% and 7% on total sales must bridge ₹3860 down to the net advantage of ₹620: (13% - 7%) of S = 3860 - 620 6% of S = 3240 ==> S = 3240 / 0.06 = ₹54,000. Atah sahi uttar (d) hai.
A marketing agent earns 2% commission on the first ₹2,00,000 of sales, 1.5% on the next ₹2,00,000, and 1% on any remaining balance in a month. If the total sales generated in April 2018 were ₹5,68,000, what was the total commission earned?
एक विपणन एजेंट को महीने में पहले ₹2,00,000 की बिक्री पर 2%, अगले ₹2,00,000 पर 1.5% और शेष बिक्री पर 1% कमीशन मिलता है। यदि अप्रैल 2018 में अर्जित कुल बिक्री ₹5,68,000 थी, तो कुल कितना कमीशन मिला?
(A) (a) ₹8,680
(B) (b) ₹7,730
(C) (c) ₹8,240
(D) (d) ₹7,105
✅ Answer & Explanation
Sahi jawab: A) (a) ₹8,680Explanation: Method 1 (Slab Breakdown): - Slab 1 (First ₹2,00,000): 2% of 2,00,000 = ₹4,000 - Slab 2 (Next ₹2,00,000): 1.5% of 2,00,000 = ₹3,000 - Slab 3 (Balance sales above ₹4,00,000): 5,68,000 - 4,00,000 = ₹1,68,000 Commission = 1% of 1,68,000 = ₹1,680 Total Commission = 4000 + 3000 + 1680 = ₹8,680. Atah sahi vikalp (a) ₹8,680 hai. Method 2 (Direct Weighted Sum): Total = (200000 * 0.02) + (200000 * 0.015) + (168000 * 0.01) = 4000 + 3000 + 1680 = ₹8,680. Atah sahi uttar (a) hai.
Two saleswomen, Kavitha and Kalyani, receive 12% and 15% commission respectively on their total sales. Kavitha gets an extra 3% bonus and Kalyani gets an extra 5% bonus on sales exceeding ₹20,000. If each made the same total sales and the difference between their earnings is ₹7,600, find Kavitha's total earnings.
दो महिला विक्रेताओं, कविता और कल्याणी को कुल बिक्री पर क्रमशः 12% और 15% कमीशन मिलता है। कविता को ₹20,000 से अधिक की बिक्री पर 3% और कल्याणी को 5% अतिरिक्त बोनस मिलता है। यदि दोनों की कुल बिक्री समान है और उनकी कुल कमाई का अंतर ₹7,600 है, तो कविता की कुल कमाई ज्ञात कीजिए।
(A) (a) ₹19,200
(B) (b) ₹21,600
(C) (c) ₹17,800
(D) (d) ₹23,400
✅ Answer & Explanation
Sahi jawab: D) (d) ₹23,400Explanation: Method 1 (Algebraic Setup): Let total sales made by each be S (where S > 20000). - Kavitha's total earnings = 12% of S + 3% of (S - 20000) = 15% of S - 600 - Kalyani's total earnings = 15% of S + 5% of (S - 20000) = 20% of S - 1000 Difference in earnings (Kalyani - Kavitha): (0.20 * S - 1000) - (0.15 * S - 600) = 7600 0.05 * S - 400 = 7600 0.05 * S = 8000 ==> S = 8000 / 0.05 = ₹1,60,000. Kavitha's total earnings: = (15% of 160000) - 600 = 24000 - 600 = ₹23,400. Atah sahi vikalp (d) ₹23,400 hai. Method 2 (Rate Difference Breakdown): - On first ₹20,000: Rate difference = 15% - 12% = 3% ==> ₹600. - On sales above ₹20,000: Effective rates are (12 + 3) = 15% and (15 + 5) = 20%. Difference = 5%. Total difference = 600 + 5% of (S - 20000) = 7600 5% of (S - 20000) = 7000 ==> S - 20000 = 1,40,000 ==> S = 1,60,000. Kavitha's earnings = (12% of 160000) + (3% of 140000) = 19200 + 4200 = ₹23,400. Atah sahi uttar (d) hai.
A salesman receives a commission of a% on the first ₹3,000 worth of sales and b% on all sales beyond that. In January, his commission was ₹960 on sales of ₹7,000. In February, his commission was ₹1,110 on sales of ₹8,000. Find the values of a and b.
एक विक्रेता को पहले ₹3,000 की बिक्री पर a% तथा उससे आगे की बिक्री पर b% कमीशन मिलता है। जनवरी में ₹7,000 की बिक्री पर उसने ₹960 अर्जित किए और फरवरी में ₹8,000 की बिक्री पर ₹1,110 अर्जित किए। a और b का मान ज्ञात कीजिए।
(A) (a) 12%, 15%
(B) (b) 15%, 12%
(C) (c) 10%, 15%
(D) (d) 12%, 10%
✅ Answer & Explanation
Sahi jawab: A) (a) 12%, 15%Explanation: Method 1 (Incremental Difference Method): - Sales above ₹3,000 in January = 7000 - 3000 = ₹4,000. - Sales above ₹3,000 in February = 8000 - 3000 = ₹5,000. Increase in sales = 5000 - 4000 = ₹1,000. Increase in commission = 1110 - 960 = ₹150. Since the additional sales fall completely in the second slab: b% of 1000 = 150 ==> b = (150 / 1000) * 100% = 15%. Substitute b = 15% into January's earnings: Commission from first ₹3,000 = 960 - (15% of 4000) = 960 - 600 = ₹360. a% of 3000 = 360 ==> a = (360 / 3000) * 100% = 12%. Hence, a = 12% and b = 15%. Atah sahi vikalp (a) 12%, 15% hai. Method 2 (Simultaneous Equations): 30a + 40b = 960 --- (1) 30a + 50b = 1110 --- (2) Subtracting (1) from (2): 10b = 150 ==> b = 15%. From (1): 30a + 40(15) = 960 ==> 30a = 360 ==> a = 12%. Atah sahi uttar (a) hai.