1. Question
English: A number is divided into two parts in the ratio 7:5. If the first part is increased by 20% and the second part is decreased by 10%, the new sum becomes 690. Find the original number.
Hindi: एक संख्या को 7:5 के अनुपात में दो भागों में बाँटा गया है। यदि पहले भाग को 20% बढ़ाया जाए और दूसरे भाग को 10% घटाया जाए, तो नई राशि 690 हो जाती है। मूल संख्या ज्ञात कीजिए।
Solution
Let the two parts be:
7x and 5x
After changes:
First part = 7x × 120/100 = 8.4x
Second part = 5x × 90/100 = 4.5x
New sum:
8.4x + 4.5x = 690
12.9x = 690
x = 690/12.9
x = 53.488...
Original number:
= 12x
= 641.86 ≈ 642
Answer: None of the options is exactly correct. The correct value is approximately 642.
2. Question
English: A shopkeeper sells an article at 12% loss. If he had sold it for ₹180 more, he would have gained 8%. Find the cost price.
Hindi: एक दुकानदार किसी वस्तु को 12% हानि पर बेचता है। यदि वह उसे ₹180 अधिक में बेचता, तो उसे 8% लाभ होता। क्रय मूल्य ज्ञात कीजिए।
Solution
Difference between selling prices:
= 180
Difference between loss and gain:
= 12% + 8%
= 20%
Therefore:
20% of Cost Price = 180
Cost Price:
= 180 × 100/20
= 900
Answer: ₹900 ✅
3. Question
English: A container has 80 litres of alcohol. 20 litres are removed and replaced with water. Again 20 litres of the mixture are removed and replaced with water. Find the final quantity of alcohol.
Hindi: एक पात्र में 80 लीटर अल्कोहल है। 20 लीटर निकालकर उतना ही पानी मिलाया जाता है। फिर 20 लीटर मिश्रण निकालकर उतना ही पानी मिलाया जाता है। अंतिम अल्कोहल की मात्रा ज्ञात कीजिए।
Solution
Remaining fraction each time:
= (80 − 20)/80
= 60/80
= 3/4
After two operations:
Alcohol left
= 80 × (3/4)²
= 80 × 9/16
= 45 litres
Answer: 45 litres ✅
4. Question
English: A man rows 24 km downstream and 12 km upstream in 4 hours. He can also row 12 km downstream and 24 km upstream in 5 hours. Find the speed of the stream.
Hindi: एक व्यक्ति 24 किमी धारा की दिशा में और 12 किमी धारा के विपरीत 4 घंटे में जाता है। वह 12 किमी धारा की दिशा में और 24 किमी धारा के विपरीत 5 घंटे में भी जाता है। धारा की चाल ज्ञात कीजिए।
Solution
Let:
Speed in still water = b km/h
Speed of stream = s km/h
Then:
24/(b+s) + 12/(b−s) = 4
12/(b+s) + 24/(b−s) = 5
Solving:
b = 4 km/h
s = 2 km/h
Answer: 2 km/h ✅
5. Question
English: A train crosses a 300 m platform in 30 seconds and a 180 m bridge in 24 seconds. Find the length of the train.
Hindi: एक ट्रेन 300 मीटर लंबे प्लेटफॉर्म को 30 सेकंड में और 180 मीटर लंबे पुल को 24 सेकंड में पार करती है। ट्रेन की लंबाई ज्ञात कीजिए।
Solution
Let train length = L
Speed = v
L + 300 = 30v
L + 180 = 24v
Subtract:
120 = 6v
v = 20 m/s
Now:
L + 180 = 24 × 20
L + 180 = 480
L = 300 m
Answer: 300 m ✅
6. Question
English: A alone can complete a work in 16 days. B is 25% more efficient than A. In how many days will A and B together complete the work?
Hindi: A अकेले किसी कार्य को 16 दिनों में पूरा कर सकता है। B, A से 25% अधिक दक्ष है। A और B मिलकर कार्य को कितने दिनों में पूरा करेंगे?
Solution
A's efficiency = 1/16
B is 25% more efficient:
B's efficiency
= 125% of 1/16
= 5/64
Together:
= 1/16 + 5/64
= 4/64 + 5/64
= 9/64
Time:
= 64/9 days
Answer: 64/9 days ✅
7. Question
English: A sum is lent at compound interest. It becomes ₹15625 in 2 years and ₹19531.25 in 3 years. Find the rate of interest per annum.
Hindi: एक राशि चक्रवृद्धि ब्याज पर दी गई है। यह 2 वर्षों में ₹15625 और 3 वर्षों में ₹19531.25 हो जाती है। वार्षिक ब्याज दर ज्ञात कीजिए।
Solution
One-year growth factor:
= 19531.25 / 15625
= 1.25
Rate:
= 25%
Answer: 25% ✅
8. Question
English: The average of 9 consecutive odd numbers is 45. Find the product of the smallest and largest numbers.
Hindi: 9 क्रमागत विषम संख्याओं का औसत 45 है। सबसे छोटी और सबसे बड़ी संख्या का गुणनफल ज्ञात कीजिए।
Solution
Middle number = 45
Nine consecutive odd numbers:
37, 39, 41, 43, 45, 47, 49, 51, 53
Smallest = 37
Largest = 53
Product:
= 37 × 53
= 1961
Answer: 1961
Note: Given answer key (2021) is incorrect.
9. Question
English: The total cost of 5 pens and 8 notebooks is ₹430. The cost of 3 pens and 4 notebooks is ₹230. Find the cost of 1 notebook.
Hindi: 5 पेन और 8 कॉपियों की कुल कीमत ₹430 है। 3 पेन और 4 कॉपियों की कीमत ₹230 है। 1 कॉपी की कीमत ज्ञात कीजिए।
Solution
Let:
Pen = p
Notebook = n
5p + 8n = 430
3p + 4n = 230
Multiply second equation by 2:
6p + 8n = 460
Subtract:
p = 30
Now:
3(30) + 4n = 230
90 + 4n = 230
4n = 140
n = 35
Answer: ₹35 ✅
10. Question
English: A person saves 25% of his income. If his income increases by 40% and savings increase by 60%, find the percentage increase in his expenditure.
Hindi: एक व्यक्ति अपनी आय का 25% बचाता है। यदि उसकी आय 40% बढ़ती है और बचत 60% बढ़ती है, तो उसके खर्च में प्रतिशत वृद्धि ज्ञात कीजिए।
Solution
Let income = 100
Savings = 25
Expenditure = 75
New income:
= 140
New savings:
= 25 × 1.6
= 40
New expenditure:
= 140 − 40
= 100
Increase in expenditure:
= 100 − 75
= 25
Percentage increase:
= 25/75 × 100
= 33⅓%
Answer: 33⅓% ✅
11. Question
English: A contractor undertakes to complete a work in 40 days with 30 workers. After 10 days, only 1/4 of the work is completed. How many additional workers are required to finish the work on time?
Hindi: एक ठेकेदार 30 मजदूरों के साथ 40 दिनों में कार्य पूरा करने का ठेका लेता है। 10 दिनों के बाद केवल 1/4 कार्य पूरा होता है। समय पर कार्य पूरा करने के लिए कितने अतिरिक्त मजदूर चाहिए?
Solution
Total work = 1
Work completed in first 10 days = 1/4
Remaining work = 3/4
Remaining time = 40 − 10
= 30 days
30 workers completed 1/4 work in 10 days.
Required rate for remaining work:
= (3/4)/30
= 1/40 per day
Current workers' rate:
= (1/4)/10
= 1/40 per day
Current workforce is already sufficient.
Additional workers required:
= 0
Answer: 0 ✅
12. Question
English: A sum of ₹4800 is divided among A, B and C such that A gets 25% more than B and B gets 20% less than C. Find C’s share.
Hindi: ₹4800 को A, B और C में इस प्रकार बाँटा गया कि A को B से 25% अधिक और B को C से 20% कम मिलता है। C का हिस्सा ज्ञात कीजिए।
Solution
Let B = 100 units
Then:
A = 125 units
B = 100 units
Since B is 20% less than C:
C = 125 units
Ratio:
A : B : C
= 125 : 100 : 125
= 5 : 4 : 5
Total parts:
= 14
One part:
= 4800/14
= 2400/7
C's share:
= 5 × 2400/7
= 12000/7
≈ ₹1714.29
Answer: ₹1714.29
Note: Given answer key (₹2000) is incorrect.
13. Question
English: A person sold an article at 16% profit. If the cost price and selling price were both ₹120 less, the profit would have been 20%. Find the original cost price.
Hindi: एक व्यक्ति ने किसी वस्तु को 16% लाभ पर बेचा। यदि क्रय मूल्य और विक्रय मूल्य दोनों ₹120 कम होते, तो लाभ 20% होता। मूल क्रय मूल्य ज्ञात कीजिए।
Solution
Let original cost price = x
Selling price = 1.16x
After reducing both by ₹120:
New cost price = x − 120
New selling price = 1.16x − 120
Given profit becomes 20%
1.16x − 120 = 1.20(x − 120)
1.16x − 120 = 1.20x − 144
24 = 0.04x
x = 600
Original cost price = ₹600
Answer: ₹600
Note: Given answer key (₹720) is incorrect.
14. Question
English: A mixture of 40 litres contains milk and water in the ratio 3:2. How much water should be evaporated so that the ratio becomes 2:1?
Hindi: 40 लीटर मिश्रण में दूध और पानी का अनुपात 3:2 है। अनुपात 2:1 करने के लिए कितना पानी वाष्पित करना होगा?
Solution
Milk:
= 40 × 3/5
= 24 litres
Water:
= 40 × 2/5
= 16 litres
Let x litres water evaporate.
New water:
= 16 − x
Required ratio:
24 : (16 − x)
= 2 : 1
24 = 2(16 − x)
24 = 32 − 2x
2x = 8
x = 4
Answer: 4 litres ✅
15. Question
English: A man can walk a certain distance in 6 hours. If he increases his speed by 2 km/h, he covers the same distance in 4 hours. Find the distance.
Hindi: एक व्यक्ति एक निश्चित दूरी 6 घंटे में तय करता है। यदि वह अपनी चाल 2 km/h बढ़ा दे, तो वही दूरी 4 घंटे में तय करता है। दूरी ज्ञात कीजिए।
Solution
Let original speed = x km/h
Distance:
= 6x
Also:
Distance = 4(x + 2)
Therefore:
6x = 4x + 8
2x = 8
x = 4
Distance:
= 6 × 4
= 24 km
Answer: 24 km ✅
16. Question
English: In a class, 60% students passed in Mathematics and 70% passed in English. If 20% failed in both subjects, what percentage passed in both subjects?
Hindi: एक कक्षा में 60% छात्र गणित में और 70% छात्र अंग्रेजी में पास हुए। यदि 20% दोनों विषयों में फेल हुए, तो दोनों विषयों में पास होने वाले छात्रों का प्रतिशत ज्ञात कीजिए।
Solution
Failed in both:
= 20%
Passed at least one subject:
= 100 − 20
= 80%
Using formula:
Math + English − Both
= At least one
60 + 70 − Both
= 80
130 − Both = 80
Both = 50
Answer: 50% ✅
17. Question
English: A sum is invested at 10% simple interest and another equal sum at 12% simple interest. After 5 years, the total interest is ₹5500. Find each sum.
Hindi: एक राशि 10% साधारण ब्याज पर और उतनी ही राशि 12% साधारण ब्याज पर निवेश की जाती है। 5 वर्षों बाद कुल ब्याज ₹5500 है। प्रत्येक राशि ज्ञात कीजिए।
Solution
Let each sum = x
Interest from first sum:
= x × 10 × 5 /100
= x/2
Interest from second sum:
= x × 12 × 5 /100
= 3x/5
Total interest:
x/2 + 3x/5 = 5500
5x + 6x = 55000
11x = 55000
x = 5000
Answer: ₹5000 ✅
18. Question
English: A, B and C started a business. A invested ₹12000 for 12 months, B invested ₹15000 for 8 months and C invested ₹20000 for 6 months. If total profit is ₹27000, find B’s profit.
Hindi: A, B और C ने व्यापार शुरू किया। A ने ₹12000 को 12 महीने, B ने ₹15000 को 8 महीने और C ने ₹20000 को 6 महीने के लिए लगाया। यदि कुल लाभ ₹27000 है, तो B का लाभ ज्ञात कीजिए।
Solution
Capital × Time:
A = 12000 × 12 = 144000
B = 15000 × 8 = 120000
C = 20000 × 6 = 120000
Ratio:
144000 : 120000 : 120000
= 6 : 5 : 5
Total parts:
= 16
B’s share:
= 27000 × 5/16
= ₹8437.50
Answer: ₹8437.50
Note: Given answer key (₹9000) is incorrect.
19. Question
English: A clock loses 2 minutes every hour. If it is set correct at 6:00 AM, what time will it show when the correct time is 9:00 PM on the same day?
Hindi: एक घड़ी हर घंटे 2 मिनट पीछे हो जाती है। यदि उसे सुबह 6:00 बजे सही किया गया, तो उसी दिन रात 9:00 बजे सही समय होने पर वह क्या समय दिखाएगी?
Solution
Time elapsed:
6 AM to 9 PM
= 15 hours
Loss per hour:
= 2 minutes
Total loss:
= 15 × 2
= 30 minutes
Therefore clock will show:
9:00 PM − 30 minutes
= 8:30 PM
Answer: 8:30 PM ✅
20. Question
English: The marked price of an article is 60% above its cost price. After giving a discount of 25%, the shopkeeper earns ₹240 profit. Find the cost price.
Hindi: एक वस्तु का अंकित मूल्य उसके क्रय मूल्य से 60% अधिक है। 25% छूट देने के बाद दुकानदार को ₹240 लाभ होता है। क्रय मूल्य ज्ञात कीजिए।
Solution
Let cost price = x
Marked price:
= 1.6x
After 25% discount:
Selling price
= 1.6x × 75/100
= 1.2x
Profit:
= 1.2x − x
= 0.2x
Given:
0.2x = 240
x = 1200
Answer: ₹1200 ✅
21. Question
English: Two numbers are in the ratio 8:11. If 7 is added to each, the ratio becomes 3:4. Find the smaller number.
Hindi: दो संख्याएँ 8:11 के अनुपात में हैं। यदि दोनों में 7 जोड़ा जाए, तो अनुपात 3:4 हो जाता है। छोटी संख्या ज्ञात कीजिए।
Solution
Let the numbers be:
8x and 11x
After adding 7:
(8x + 7)/(11x + 7) = 3/4
4(8x + 7) = 3(11x + 7)
32x + 28 = 33x + 21
x = 7
Smaller number:
= 8x
= 8 × 7
= 56
Answer: 56 ✅
22. Question
English: A alone can complete a work in 30 days. B alone can complete the same work in 45 days. A works for 10 days and then B works for 15 days. What fraction of the work is left?
Hindi: A अकेले किसी कार्य को 30 दिनों में पूरा कर सकता है। B अकेले उसी कार्य को 45 दिनों में पूरा कर सकता है। A 10 दिन काम करता है और फिर B 15 दिन काम करता है। कार्य का कितना भाग शेष है?
Solution
A’s 1-day work:
= 1/30
A’s work in 10 days:
= 10/30
= 1/3
B’s 1-day work:
= 1/45
B’s work in 15 days:
= 15/45
= 1/3
Total work done:
= 1/3 + 1/3
= 2/3
Remaining work:
= 1 - 2/3
= 1/3
Answer: 1/3 ✅
23. Question
English: A man sells 60% of his goods at 20% profit and the remaining at 10% loss. Find his overall profit percentage.
Hindi: एक व्यक्ति अपने माल का 60% भाग 20% लाभ पर और शेष भाग 10% हानि पर बेचता है। कुल लाभ प्रतिशत ज्ञात कीजिए।
Solution
Let total cost price = 100
Cost of 60% goods:
= 60
Selling price at 20% profit:
= 60 × 120/100
= 72
Cost of remaining 40% goods:
= 40
Selling price at 10% loss:
= 40 × 90/100
= 36
Total selling price:
= 72 + 36
= 108
Profit:
= 108 - 100
= 8
Profit percentage:
= 8%
Answer: 8% ✅
24. Question
English: A candidate scores 45% marks and fails by 20 marks. Another candidate scores 55% marks and gets 30 marks more than the passing marks. Find the maximum marks.
Hindi: एक अभ्यर्थी 45% अंक प्राप्त करता है और 20 अंकों से असफल होता है। दूसरा अभ्यर्थी 55% अंक प्राप्त करता है और उत्तीर्णांक से 30 अंक अधिक पाता है। अधिकतम अंक ज्ञात कीजिए।
Solution
Let maximum marks = x
First candidate gets:
45% of x
He fails by 20 marks.
So passing marks:
= 45% of x + 20
Second candidate gets:
55% of x
He gets 30 more than passing marks.
So passing marks:
= 55% of x - 30
Now both passing marks are equal:
45% of x + 20 = 55% of x - 30
50 = 10% of x
x = 500
Answer: 500 ✅
25. Question
English: The cost of 6 chairs and 4 tables is ₹18000, while the cost of 4 chairs and 6 tables is ₹22000. Find the cost of 1 table.
Hindi: 6 कुर्सियों और 4 मेजों की कीमत ₹18000 है, जबकि 4 कुर्सियों और 6 मेजों की कीमत ₹22000 है। 1 मेज की कीमत ज्ञात कीजिए।
Solution
Let:
Cost of 1 chair = ₹C
Cost of 1 table = ₹T
Given:
6C + 4T = 18000
4C + 6T = 22000
Multiply first equation by 3:
18C + 12T = 54000
Multiply second equation by 2:
8C + 12T = 44000
Subtract:
10C = 10000
C = 1000
Now substitute in:
6C + 4T = 18000
6 × 1000 + 4T = 18000
6000 + 4T = 18000
4T = 12000
T = 3000
Answer
1 table = ₹3000