Ratio, Average & Mixture: Practice Questions with Answers

Ratio and proportion, ages, averages and mixtures. Try each question first: tap an option to check it, and the explanation appears below.

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Question 1Medium
The average of 14 numbers is 38. When one more number is added, the average becomes 39. What is the number added?
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✅ A. 53
Total of the 14 numbers = 14 × 38 = 532. Total of all 15 numbers = 15 × 39 = 585. The new number is the difference: 585 − 532 = 53. Shortcut: new number = new average + (old count × rise in average) = 39 + 14 × 1 = 53.
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Question 2Hard
A 180-litre mixture contains milk and water in the ratio 7 : 3. How many litres of water must be added to make the ratio 3 : 2?
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✅ A. 30 litres
Milk = 180 × 7/10 = 126 litres and water = 54 litres. Adding water does not change the milk. For milk : water = 3 : 2, the water must be 126 × 2/3 = 84 litres. So add 84 − 54 = 30 litres of water.
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Question 3Medium
In what ratio must lentils costing ₹56 per kg be mixed with lentils costing ₹67 per kg, so that the mixture is worth ₹64 per kg?
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✅ C. 3 : 8
Use alligation: the cheaper part : the dearer part = (dearer price − mixture price) : (mixture price − cheaper price) = (67 − 64) : (64 − 56) = 3 : 8, which simplifies to 3 : 8. Check: mixing in that ratio gives an average of ₹64 per kg. Writing the differences the other way round is the most common mistake.
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Question 4Medium
In what ratio must rice costing ₹53 per kg be mixed with rice costing ₹65 per kg, so that the mixture is worth ₹55 per kg?
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✅ D. 5 : 1
Use alligation: the cheaper part : the dearer part = (dearer price − mixture price) : (mixture price − cheaper price) = (65 − 55) : (55 − 53) = 10 : 2, which simplifies to 5 : 1. Check: mixing in that ratio gives an average of ₹55 per kg. Writing the differences the other way round is the most common mistake.
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Question 5Hard
The average of 13 results is 39. The average of the first 7 results is 45 and the average of the last 7 results is 41. What is the 7th result?
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✅ B. 95
The first 7 and the last 7 results together make 14 results, but there are only 13: the 7th result is counted in both groups. Sum of the first 7 = 7 × 45 = 315; sum of the last 7 = 7 × 41 = 287; sum of all 13 = 13 × 39 = 507. So the 7th result = 315 + 287 − 507 = 95.
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Question 6Easy
An amount of ₹18,850 is shared among P, Q and R in the ratio 6 : 3 : 4. How much does R get?
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✅ C. ₹5,800
Total parts = 6 + 3 + 4 = 13. One part = ₹18,850 ÷ 13 = ₹1,450. R's share = 4 parts = ₹5,800. P gets ₹8,700 and Q gets ₹4,350, and the three shares add up to ₹18,850.
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Question 7Easy
₹9,010 is divided between A and B in the ratio 9 : 8. What is B's share?
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✅ A. ₹4,240
The ratio 9 : 8 has 17 parts in total. One part = ₹9,010 ÷ 17 = ₹530. B gets 8 parts = 8 × ₹530 = ₹4,240, and A gets ₹4,770. Check: ₹4,240 + ₹4,770 = ₹9,010.
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Question 8Medium
The average of 8 numbers is 38. When one more number is added, the average becomes 41. What is the number added?
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✅ A. 65
Total of the 8 numbers = 8 × 38 = 304. Total of all 9 numbers = 9 × 41 = 369. The new number is the difference: 369 − 304 = 65. Shortcut: new number = new average + (old count × rise in average) = 41 + 8 × 3 = 65.
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Question 9Easy
₹3,800 is divided between A and B in the ratio 9 : 1. What is B's share?
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✅ A. ₹380
The ratio 9 : 1 has 10 parts in total. One part = ₹3,800 ÷ 10 = ₹380. B gets 1 parts = 1 × ₹380 = ₹380, and A gets ₹3,420. Check: ₹380 + ₹3,420 = ₹3,800.
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Question 10Medium
The average weight of 16 students increases by 1.5 kg when one student weighing 44 kg is replaced by a new student. What is the weight of the new student?
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✅ C. 68 kg
If the average rises by 1.5 kg for 16 students, the total weight rises by 16 × 1.5 = 24 kg. The only change is the swap, so the new student weighs 24 kg more than the one who left: 44 + 24 = 68 kg.
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Question 11Hard
A 160-litre mixture contains milk and water in the ratio 7 : 3. How many litres of water must be added to make the ratio 2 : 1?
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✅ B. 8 litres
Milk = 160 × 7/10 = 112 litres and water = 48 litres. Adding water does not change the milk. For milk : water = 2 : 1, the water must be 112 × 1/2 = 56 litres. So add 56 − 48 = 8 litres of water.
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Question 12Easy
₹920 is divided between A and B in the ratio 3 : 1. What is B's share?
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✅ A. ₹230
The ratio 3 : 1 has 4 parts in total. One part = ₹920 ÷ 4 = ₹230. B gets 1 parts = 1 × ₹230 = ₹230, and A gets ₹690. Check: ₹230 + ₹690 = ₹920.
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Question 13Easy
What is the average of the first 51 odd numbers?
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✅ A. 51
The sum of the first n odd numbers is n², so here it is 51² = 2601. Average = 2601 ÷ 51 = 51. For any evenly spaced list, the average is also the middle of the first and last numbers.
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Question 14Medium
The average of 9 numbers is 24. When one more number is added, the average becomes 29. What is the number added?
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✅ D. 74
Total of the 9 numbers = 9 × 24 = 216. Total of all 10 numbers = 10 × 29 = 290. The new number is the difference: 290 − 216 = 74. Shortcut: new number = new average + (old count × rise in average) = 29 + 9 × 5 = 74.
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Question 15Medium
What is the mean proportional between 144 and 36?
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✅ C. 72
The mean proportional between two numbers a and b is √(a × b). Here √(144 × 36) = √5184 = 72. Check: 144 : 72 = 72 : 36, because 144 × 36 = 72 × 72 = 5184. The average (90) is a different idea.
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Question 16Medium
What is the mean proportional between 144 and 196?
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✅ C. 168
The mean proportional between two numbers a and b is √(a × b). Here √(144 × 196) = √28224 = 168. Check: 144 : 168 = 168 : 196, because 144 × 196 = 168 × 168 = 28224. The average (170) is a different idea.
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Question 17Medium
The average weight of 17 students increases by 1 kg when one student weighing 47 kg is replaced by a new student. What is the weight of the new student?
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✅ B. 64 kg
If the average rises by 1 kg for 17 students, the total weight rises by 17 × 1 = 17 kg. The only change is the swap, so the new student weighs 17 kg more than the one who left: 47 + 17 = 64 kg.
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Question 18Hard
The average of 9 results is 47. The average of the first 5 results is 53 and the average of the last 5 results is 51. What is the 5th result?
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✅ D. 97
The first 5 and the last 5 results together make 10 results, but there are only 9: the 5th result is counted in both groups. Sum of the first 5 = 5 × 53 = 265; sum of the last 5 = 5 × 51 = 255; sum of all 9 = 9 × 47 = 423. So the 5th result = 265 + 255 − 423 = 97.
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Question 19Hard
A container holds 60 litres of milk. 12 litres are taken out and replaced with water. This is done once more. How much milk is now in the container?
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✅ B. 38.4 litres
Each time, 12 of the 60 litres is removed, so 48/60 of the milk stays. After the first time: 60 × 48/60 = 48 litres of milk. After the second time: 48 × 48/60 = 38.4 litres. Formula: milk left = V × (1 − x/V)ⁿ for n repetitions. Subtracting 12 twice (36 litres) is wrong because the second removal takes out some water too.
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Question 20Medium
The ages of A and B are in the ratio 3 : 4. After 12 years, the ratio of their ages will be 33 : 40. What is A's present age?
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✅ D. 21 years
Let the present ages be 3x and 4x. After 12 years: (3x + 12) : (4x + 12) = 33 : 40. Cross-multiplying: 40(3x + 12) = 33(4x + 12), which gives 12x = 84, so x = 7. A's present age is 3 × 7 = 21 years (and B's is 28). Check: after 12 years they are 33 and 40, which is 33 : 40.
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Ratio, Average & Mixture: Practice Questions with Answers

The average of 14 numbers is 38. When one more number is added, the average becomes 39. What is the number added?

A 180-litre mixture contains milk and water in the ratio 7 : 3. How many litres of water must be added to make the ratio 3 : 2?

In what ratio must lentils costing ₹56 per kg be mixed with lentils costing ₹67 per kg, so that the mixture is worth ₹64 per kg?

In what ratio must rice costing ₹53 per kg be mixed with rice costing ₹65 per kg, so that the mixture is worth ₹55 per kg?

The average of 13 results is 39. The average of the first 7 results is 45 and the average of the last 7 results is 41. What is the 7th result?

An amount of ₹18,850 is shared among P, Q and R in the ratio 6 : 3 : 4. How much does R get?

₹9,010 is divided between A and B in the ratio 9 : 8. What is B's share?

The average of 8 numbers is 38. When one more number is added, the average becomes 41. What is the number added?

₹3,800 is divided between A and B in the ratio 9 : 1. What is B's share?

The average weight of 16 students increases by 1.5 kg when one student weighing 44 kg is replaced by a new student. What is the weight of the new student?

A 160-litre mixture contains milk and water in the ratio 7 : 3. How many litres of water must be added to make the ratio 2 : 1?

₹920 is divided between A and B in the ratio 3 : 1. What is B's share?

What is the average of the first 51 odd numbers?

The average of 9 numbers is 24. When one more number is added, the average becomes 29. What is the number added?

What is the mean proportional between 144 and 36?

What is the mean proportional between 144 and 196?

The average weight of 17 students increases by 1 kg when one student weighing 47 kg is replaced by a new student. What is the weight of the new student?

The average of 9 results is 47. The average of the first 5 results is 53 and the average of the last 5 results is 51. What is the 5th result?

A container holds 60 litres of milk. 12 litres are taken out and replaced with water. This is done once more. How much milk is now in the container?

The ages of A and B are in the ratio 3 : 4. After 12 years, the ratio of their ages will be 33 : 40. What is A's present age?