Ratio and proportion

2012 · Q62

Two glasses of equal volume are respectively half and three-fourths filled with milk. They are then filled to the brim by adding water. Their contents are then poured into another vessel. What will be the ratio of milk to water in this vessel?

1. (a)1: 3
2. (b)2: 3
3. (c)3: 2
4. (d)5: 3UPSC key

2013 · Q31

There are some balls of red, green and yellow colour lying on a table. There are as many red balls as there are yellow balls. There are twice as many yellow balls as there are green ones. The number of red balls

1. (a)is equal to the sum of yellow and green balls.
2. (b)is double the number of green balls.UPSC key
3. (c)is equal to yellow balls minus green balls.
4. (d)cannot be ascertained.

2013 · Q60

In a rare coin collection, there is one gold coin for every three non-gold coins. 10 more gold coins are added to the collection and the ratio of gold coins to non-gold coins would be 1: 2. Based on the information, the total number of coins in the collection now becomes

1. (a)90UPSC key
2. (b)80
3. (c)60
4. (d)50

2013 · Q64

In a garrison, there was food for 1000 soldiers for one month. After 10 days, 1000 more soldiers joined the garrison. How long would the soldiers be able to carry on with the remaining food?

1. (a)25 days
2. (b)20 days
3. (c)15 days
4. (d)10 daysUPSC key

2015 · Q10

An automobile owner reduced his monthly petrol consumption when the prices went up. The price-consumption relationship is as follows:

If the price goes up to ₹ 80 per litre, his expected consumption (in litres) will be

1. (a)30UPSC key
2. (b)28
3. (c)26
4. (d)24

2015 · Q35

Two equal glasses of same type are respectively $\dfrac{1}{3}$ and $\dfrac{1}{4}$ full of milk. They are then filled up with water and the contents are mixed in a pot. What is the ratio of milk and water in the pot?

1. (a)7: 17UPSC key
2. (b)1: 3
3. (c)9: 21
4. (d)11: 23

2015 · Q70

The monthly incomes of Peter and Paul are in the ratio of 4: 3. Their expenses are in the ratio of 3: 2. If each saves ₹ 6,000 at the end of the month, their monthly incomes respectively are (in ₹)

1. (a)24,000 and 18,000UPSC key
2. (b)28,000 and 21,000
3. (c)32,000 and 24,000
4. (d)34,000 and 26,000

2016 · Q28

30 g of sugar was mixed in 180 ml water in a vessel A, 40 g of sugar was mixed in 280 ml of water in vessel B and 20 g of sugar was mixed in 100 ml of water in vessel C. The solution in vessel B is:

1. (a)sweeter than that in C
2. (b)sweeter than that in A
3. (c)as sweet as that in C
4. (d)less sweet than that in CUPSC key

2016 · Q31

In a class, there are 18 very tall boys. If these constitute three-fourths of the boys and the total number of boys is two-thirds of the total number of students in the class, what is the number of girls in the class?

1. (a)6
2. (b)12UPSC key
3. (c)18
4. (d)21

2016 · Q52

The total emoluments of two persons are the same, but one gets allowances to the extent of 65% of his basic pay and the other gets allowances to the extent of 80% of his basic pay. The ratio of the basic pay of the former to the basic pay of the latter is:

1. (a)16: 13
2. (b)5: 4
3. (c)7: 5
4. (d)12: 11UPSC key

2017 · Q37

There is a milk sample with 50% water in it. If 1/3rd of this milk is added to equal amount of pure milk, then water in the new mixture will fall down to

1. (a)25%UPSC key
2. (b)30%
3. (c)35%
4. (d)40%

2017 · Q74

The monthly incomes of X and Y are in the ratio of 4: 3 and their monthly expenses are in the ratio of 3: 2. However, each saves ₹ 6,000 per month. What is their total monthly income?

1. (a)₹ 28,000
2. (b)₹ 42,000UPSC key
3. (c)₹ 56,000
4. (d)₹ 84,000

2018 · Q68

A lift has the capacity of 18 adults or 30 children. How many children can board the lift with 12 adults?

1. (a)6
2. (b)10UPSC key
3. (c)12
4. (d)15

2020 · Q57

A sum of ₹ 2,500 is distributed among X, Y and Z in the ratio $\dfrac{1}{2}$: $\dfrac{3}{4}$: $\dfrac{5}{6}$. What is the difference between the maximum share and the minimum share?

1. (a)₹ 300
2. (b)₹ 350
3. (c)₹ 400UPSC key
4. (d)₹ 450

2020 · Q68

A bottle contains 20 litres of liquid A. 4 litres of liquid A is taken out of it and replaced by same quantity of liquid B. Again 4 litres of the mixture is taken out and replaced by same quantity of liquid B. What is the ratio of quantity of liquid A to that of liquid B in the final mixture?

1. (a)4: 1
2. (b)5: 1
3. (c)16: 9UPSC key
4. (d)17: 8

2021 · Q30

A student appeared in 6 papers. The maximum marks are the same for each paper. His marks in these papers are in the proportion of 5: 6: 7: 8: 9: 10. Overall he scored 60%. In how many number of papers did he score less than 60% of the maximum marks?

1. (a)2
2. (b)3UPSC key
3. (c)4
4. (d)5

2021 · Q70

An amount of money was distributed among A, B and C in the ratio p: q: r.

Consider the following statements:

1.A gets the maximum share if p is greater than (q + r).

2.C gets the minimum share if r is less than (p + q).

Which of the above statements is/are correct?

1. (a)1 onlyUPSC key
2. (b)2 only
3. (c)Both 1 and 2
4. (d)Neither 1 nor 2

2022 · Q69

There are two containers X and Y. X contains 100 ml of milk and Y contains 100 ml of water. 20 ml of milk from X is transferred to Y. After mixing well, 20 ml of the mixture in Y is transferred back to X. If m denotes the proportion of milk in X and n denotes the proportion of water in Y, then which one of the following is correct?

1. (a)m = nUPSC key
2. (b)m > n
3. (c)m < n
4. (d)Cannot be determined due to insufficient data

2024 · Q25

Two persons P and Q enter into a business. P puts ₹ 14,000 more than Q, but P has invested for 8 months and Q has invested for 10 months. If P’s share is ₹ 400 more than Q’s share out of the total profit of ₹ 2,000, what is the capital contributed by P?

1. (a)₹ 30,000UPSC key
2. (b)₹ 26,000
3. (c)₹ 24,000
4. (d)₹ 20,000

2025 · Q75

In a T20 cricket match, three players X, Y and Z scored a total of 37 runs. The ratio of number of runs scored by X to the number of runs scored by Y is equal to ratio of number of runs scored by Y to number of runs scored by Z.

Value-I = Runs scored by X

Value-II = Runs scored by Y

Value-III = Runs scored by Z

Which one of the following is correct?

1. (a)Value-I < Value-II < Value-III
2. (b)Value-III < Value-II < Value-I
3. (c)Value-I < Value-III < Value-II
4. (d)Cannot be determined due to insufficient dataUPSC key

2026 · Q30

Suppose x, y and z are variables taking positive real numbers as their possible values. It is given that y is directly proportional to $x^{2}$ and x is inversely proportional to z. For z = $\dfrac{7}{25}$, the values of x and y are 5 and 50, respectively. If y = 98, what is z equal to?

1. (a)$\dfrac{1}{7}$
2. (b)$\dfrac{1}{5}$UPSC key
3. (c)$\dfrac{5}{7}$
4. (d)1

2026 · Q58

The ratio of male to female workers in two companies A and B is 13: 10 and 7: 5, respectively. If both the companies have the same number of female workers, then what is the ratio of the total number of workers in A to those in B?

1. (a)24: 23
2. (b)23: 24UPSC key
3. (c)18: 17
4. (d)27: 18

2026 · Q65

An alloy P contains 20% copper and 80% zinc by weight. Another alloy Q contains 60% copper and 40% zinc by weight. A third alloy R is to be prepared from P and Q so that it contains equal amount of copper and zinc. In what ratio, amounts of P and Q be mixed in order to get R?

1. (a)1: 3UPSC key
2. (b)3: 1
3. (c)2: 3
4. (d)3: 2

2026 · Q78

Three partners A, B and C entered into a business. A invested one-third of the capital for one-third duration. B invested one-fourth of the capital for one-fourth duration. C invested the remaining capital for the whole duration. Out of a profit of ₹17,000, how much profit will C get?

1. (a)₹12,000UPSC key
2. (b)₹10,000
3. (c)₹12,500
4. (d)₹10,750

2026 · Q79

There are two chemicals which do not react with each other. A container contains 10 litres of the chemical A. One litre of this chemical is removed from it and one litre of the chemical B is poured. Then one litre of the mixture is removed from the container and one litre of B is poured. If this process of replacing one litre of the mixture by one litre of B is performed once more, then what is the volume of B that is present in the container approximately (in percentage)?

1. (a)25
2. (b)27UPSC key
3. (c)29
4. (d)31