1. Question
English: A number when divided by 296 leaves remainder 75. What remainder will be left when the same number is divided by 37?
Hindi: एक संख्या को 296 से भाग देने पर 75 शेष बचता है। उसी संख्या को 37 से भाग देने पर शेषफल क्या होगा?
Solution:
296 is divisible by 37.
296 = 37 × 8
Number gives remainder 75 when divided by 296.
So number can be written as:
296k + 75
Now divide by 37.
296k is exactly divisible by 37.
So only 75 matters.
75 divided by 37 leaves remainder 1.
Answer: 1
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2. Question
English: If 20% of A = 30% of B and B = 40% of C, then A : C equals:
Hindi: यदि A का 20% = B का 30% और B = C का 40% है, तो A : C ज्ञात कीजिए।
Solution:
20% of A = 30% of B
20A = 30B
2A = 3B
A : B = 3 : 2
Also:
B = 40% of C
B = 2/5 C
So:
B : C = 2 : 5
Since A : B = 3 : 2 and B : C = 2 : 5
A : C = 3 : 5
Answer: 3 : 5
Note: Given answer key says 3 : 2, but correct answer is 3 : 5.
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3. Question
English: The average of 11 numbers is 48. If the average of first 6 numbers is 42 and that of last 6 numbers is 54, find the middle number.
Hindi: 11 संख्याओं का औसत 48 है। यदि पहली 6 संख्याओं का औसत 42 और अंतिम 6 संख्याओं का औसत 54 है, तो बीच की संख्या ज्ञात कीजिए।
Solution:
Sum of 11 numbers:
= 11 × 48
= 528
Sum of first 6 numbers:
= 6 × 42
= 252
Sum of last 6 numbers:
= 6 × 54
= 324
When we add first 6 and last 6, the middle number is counted twice.
So:
252 + 324 = 576
Middle number:
= 576 - 528
= 48
Answer: 48
Note: Given answer key says 60, but correct answer is 48.
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4. Question
English: A shopkeeper mixes two varieties of rice costing ₹48/kg and ₹60/kg in the ratio 5:3. Find the cost price of mixture per kg.
Hindi: एक दुकानदार ₹48/किग्रा और ₹60/किग्रा वाले चावल को 5:3 के अनुपात में मिलाता है। मिश्रण का प्रति किग्रा क्रय मूल्य ज्ञात कीजिए।
Solution:
Cost of mixture:
= (48 × 5 + 60 × 3) / (5 + 3)
= (240 + 180) / 8
= 420 / 8
= 52.5
Answer: ₹52.5
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5. Question
English: A man spends 75% of his income. His income increases by 20% and expenditure by 10%. Find the percentage increase in savings.
Hindi: एक व्यक्ति अपनी आय का 75% खर्च करता है। उसकी आय 20% बढ़ती है और खर्च 10% बढ़ता है। बचत में प्रतिशत वृद्धि ज्ञात कीजिए।
Solution:
Let income = 100
Expenditure = 75
Savings = 25
New income after 20% increase:
= 120
New expenditure after 10% increase:
= 75 + 10% of 75
= 75 + 7.5
= 82.5
New savings:
= 120 - 82.5
= 37.5
Increase in savings:
= 37.5 - 25
= 12.5
Percentage increase:
= 12.5 / 25 × 100
= 50%
Answer: 50%
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6. Question
English: The population of a town increases by 10% in first year and decreases by 10% in second year. Find the net percentage change.
Hindi: एक नगर की जनसंख्या पहले वर्ष 10% बढ़ती है और दूसरे वर्ष 10% घटती है। कुल प्रतिशत परिवर्तन ज्ञात कीजिए।
Solution:
Let population = 100
After 10% increase:
= 110
After 10% decrease:
= 110 × 90/100
= 99
Final population = 99
Original population = 100
Net change = 1 decrease
Answer: 1% decrease
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7. Question
English: A train running at 72 km/h crosses a man running at 9 km/h in opposite direction in 8 seconds. Find the length of train.
Hindi: 72 किमी/घंटा की गति से चल रही ट्रेन 9 किमी/घंटा की गति से विपरीत दिशा में दौड़ रहे व्यक्ति को 8 सेकंड में पार करती है। ट्रेन की लंबाई ज्ञात कीजिए।
Solution:
Train speed = 72 km/h
Man speed = 9 km/h
Opposite direction relative speed:
= 72 + 9
= 81 km/h
Convert into m/s:
= 81 × 5/18
= 22.5 m/s
Length of train:
= speed × time
= 22.5 × 8
= 180 m
Answer: 180 m
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8. Question
English: A sum becomes ₹8820 in 2 years and ₹9261 in 3 years at compound interest. Find the rate percent per annum.
Hindi: एक राशि 2 वर्षों में ₹8820 और 3 वर्षों में ₹9261 हो जाती है। चक्रवृद्धि ब्याज की वार्षिक दर ज्ञात कीजिए।
Solution:
Amount after 2 years = ₹8820
Amount after 3 years = ₹9261
One year growth factor:
= 9261 / 8820
= 1.05
So rate:
= 5%
Answer: 5%
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9. Question
English: If the simple interest on a sum for 5 years at 8% per annum is ₹2400, find the principal.
Hindi: यदि किसी राशि पर 5 वर्षों के लिए 8% वार्षिक दर से साधारण ब्याज ₹2400 है, तो मूलधन ज्ञात कीजिए।
Solution:
Simple interest = P × R × T / 100
2400 = P × 8 × 5 / 100
2400 = 40P / 100
2400 = 0.4P
P = 2400 / 0.4
= 6000
Answer: ₹6000
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10. Question
English: The ratio of present ages of A and B is 5:7. After 8 years, the ratio becomes 7:9. Find present age of B.
Hindi: A और B की वर्तमान आयु का अनुपात 5:7 है। 8 वर्ष बाद अनुपात 7:9 हो जाता है। B की वर्तमान आयु ज्ञात कीजिए।
Solution:
Let present ages be 5x and 7x.
After 8 years:
(5x + 8) / (7x + 8) = 7/9
9(5x + 8) = 7(7x + 8)
45x + 72 = 49x + 56
16 = 4x
x = 4
Present age of B:
= 7x
= 7 × 4
= 28 years
Answer: 28 years
Note: Given answer key says 35 years, but correct answer is 28 years.
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11. Question
English: A man can row 15 km downstream in 1 hour and 9 km upstream in 1 hour. Find speed of stream.
Hindi: एक व्यक्ति धारा के साथ 15 किमी 1 घंटे में तथा धारा के विपरीत 9 किमी 1 घंटे में तय करता है। धारा की गति ज्ञात कीजिए।
Solution:
Downstream speed = 15 km/h
Upstream speed = 9 km/h
Speed of stream:
= (15 - 9) / 2
= 6 / 2
= 3 km/h
Answer: 3 km/h
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12. Question
English: A and B together can do a work in 12 days. B and C together in 15 days. A and C together in 20 days. Find the time taken by A, B and C together.
Hindi: A और B मिलकर कार्य 12 दिनों में, B और C मिलकर 15 दिनों में तथा A और C मिलकर 20 दिनों में करते हैं। A, B और C मिलकर कार्य कितने दिनों में करेंगे?
Solution:
A + B = 1/12
B + C = 1/15
A + C = 1/20
Add all:
2(A + B + C) = 1/12 + 1/15 + 1/20
LCM = 60
= 5/60 + 4/60 + 3/60
= 12/60
= 1/5
So:
A + B + C = 1/10
Therefore, together they complete work in 10 days.
Answer: 10 days
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13. Question
English: The perimeter of a rectangle is 84 cm and its diagonal is 29 cm. Find its area.
Hindi: एक आयत का परिमाप 84 सेमी और विकर्ण 29 सेमी है। उसका क्षेत्रफल ज्ञात कीजिए।
Solution:
Let length = l and breadth = b.
Perimeter = 84
2(l + b) = 84
l + b = 42
Diagonal = 29
So:
l² + b² = 29²
= 841
Now:
(l + b)² = l² + b² + 2lb
42² = 841 + 2lb
1764 = 841 + 2lb
2lb = 923
lb = 461.5
Answer: 461.5 cm²
Note: Given options do not contain the correct answer. The data seems incorrect.
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14. Question
English: A cylinder and a cone have same base radius and same height. Find ratio of their volumes.
Hindi: एक बेलन और एक शंकु की आधार त्रिज्या तथा ऊँचाई समान है। उनके आयतनों का अनुपात ज्ञात कीजिए।
Solution:
Volume of cylinder = πr²h
Volume of cone = 1/3 × πr²h
Ratio of cylinder : cone
= πr²h : 1/3πr²h
= 3 : 1
Answer: 3 : 1
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15. Question
English: If cos θ = 12/13, then find value of tan θ.
Hindi: यदि cos θ = 12/13 है, तो tan θ का मान ज्ञात कीजिए।
Solution:
cos θ = base / hypotenuse
So:
Base = 12
Hypotenuse = 13
Perpendicular:
= 5
tan θ = perpendicular / base
= 5/12
Answer: 5/12
16. Question
English: A dealer gives two successive discounts of 10% and 20%. Find equivalent single discount.
Hindi: एक व्यापारी 10% और 20% की क्रमिक छूट देता है। तुल्य एकल छूट ज्ञात कीजिए।
Solution:
Let marked price = 100
After 10% discount:
= 90
After 20% discount:
= 90 × 80/100
= 72
Final price = 72
Total discount:
= 100 - 72
= 28
Answer: 28%
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17. Question
English: The difference between compound interest and simple interest on ₹5000 for 2 years at 10% per annum is:
Hindi: ₹5000 पर 2 वर्षों के लिए 10% वार्षिक दर से चक्रवृद्धि ब्याज और साधारण ब्याज का अंतर ज्ञात कीजिए।
Solution:
Difference between CI and SI for 2 years:
= P × R² / 10000
= 5000 × 10² / 10000
= 5000 × 100 / 10000
= 50
Answer: ₹50
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18. Question
English: A sum of money doubles itself in 8 years at simple interest. In how many years will it become three times?
Hindi: एक राशि साधारण ब्याज पर 8 वर्षों में दोगुनी हो जाती है। वह कितने वर्षों में तीन गुनी होगी?
Solution:
At simple interest, money doubles in 8 years.
That means interest equal to principal is earned in 8 years.
To become three times, interest must be 2 times the principal.
So time:
= 8 × 2
= 16 years
Answer: 16 years
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19. Question
English: How many numbers between 100 and 1000 are divisible by both 5 and 7?
Hindi: 100 और 1000 के बीच कितनी संख्याएँ 5 और 7 दोनों से विभाज्य हैं?
Solution:
A number divisible by both 5 and 7 must be divisible by 35.
Multiples of 35 between 100 and 1000:
First multiple greater than 100 = 105
Last multiple less than 1000 = 980
Now:
105 = 35 × 3
980 = 35 × 28
Number of multiples:
= 28 - 3 + 1
= 26
Answer: 26
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20. Question
English: The average weight of 8 men increases by 2.5 kg when one man of 65 kg is replaced. Find the weight of new man.
Hindi: एक 65 किग्रा व्यक्ति को बदलने पर 8 व्यक्तियों का औसत भार 2.5 किग्रा बढ़ जाता है। नए व्यक्ति का भार ज्ञात कीजिए।
Solution:
Average increase = 2.5 kg
Number of men = 8
Total weight increase:
= 2.5 × 8
= 20 kg
New man’s weight:
= old man’s weight + increase
= 65 + 20
= 85 kg
Answer: 85 kg
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21. Question
English: A man buys an article for ₹720 and sells it at a loss of 10%. At what price should he sell it to gain 20%?
Hindi: एक व्यक्ति ₹720 में वस्तु खरीदता है और 10% हानि पर बेचता है। 20% लाभ कमाने के लिए उसे किस मूल्य पर बेचना चाहिए?
Solution:
Cost price = ₹720
To gain 20%, selling price should be:
= 720 × 120/100
= 864
Answer: ₹864
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22. Question
English: A shopkeeper marks his goods 25% above cost price and gives a discount of 10%. Find his gain percent.
Hindi: एक दुकानदार वस्तु का अंकित मूल्य क्रय मूल्य से 25% अधिक रखता है और 10% छूट देता है। लाभ प्रतिशत ज्ञात कीजिए।
Solution:
Let cost price = 100
Marked price = 125
After 10% discount:
Selling price = 125 × 90/100
= 112.5
Profit = 112.5 - 100
= 12.5
Answer: 12.5%
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23. Question
English: Find the area of a rhombus whose diagonals are 24 cm and 10 cm.
Hindi: एक समचतुर्भुज की विकर्ण 24 सेमी और 10 सेमी हैं। उसका क्षेत्रफल ज्ञात कीजिए।
Solution:
Area of rhombus:
= 1/2 × product of diagonals
= 1/2 × 24 × 10
= 120
Answer: 120 cm²
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24. Question
English: A person travels 120 km at 40 km/h and returns at 60 km/h. Find average speed for whole journey.
Hindi: एक व्यक्ति 120 किमी दूरी 40 किमी/घंटा की गति से जाता है और 60 किमी/घंटा की गति से वापस आता है। पूरी यात्रा की औसत गति ज्ञात कीजिए।
Solution:
Distance going = 120 km
Time going:
= 120/40
= 3 hours
Distance returning = 120 km
Time returning:
= 120/60
= 2 hours
Total distance:
= 120 + 120
= 240 km
Total time:
= 3 + 2
= 5 hours
Average speed:
= 240/5
= 48 km/h
Answer: 48 km/h
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25. Question
English: The curved surface area of a cylinder is 440 cm² and its height is 10 cm. Find its radius.
Hindi: एक बेलन का वक्र पृष्ठीय क्षेत्रफल 440 सेमी² है और उसकी ऊँचाई 10 सेमी है। उसकी त्रिज्या ज्ञात कीजिए।
Solution:
Curved surface area of cylinder:
= 2πrh
Given:
440 = 2 × 22/7 × r × 10
440 = 440r/7
r = 7
Answer: 7 cm