How to solve GMAT Ratio and Proportion Problems?

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Are you desperately looking for practice questions on the GMAT club forum? How many questions did you find for the topic you were looking for? Are they any good?

Well, if you are scavenging for good practice questions you’ve just hit a gold mine! Problem solving comprises roughly 50% of the total questions in the GMAT quant section and in this blog, we will show you how to solve GMAT ratio and proportion problems through some quality practice questions and their detailed explanations. Let’s go!

IN THIS BLOG:

1.     GMAT Ratio and Proportion Problem 1
2.     GMAT Ratio and Proportion Problem 2
3.     GMAT Ratio and Proportion Problem 3
4.     GMAT Ratio and Proportion Problem 4
5.     GMAT Ratio and Proportion Problem 5
6.     GMAT Ratio and Proportion Problem 6

GMAT Ratio and Proportion Problem 1:

Rs.5783 is divided among Bonnie, Christy, and Violet in such a way that if Rs. 28, Rs. 37 and Rs. 18 be deducted from their respective shares, they have money in the ratio 4:6:9. Find Bonnie’s share.

1. 1256
2. 1228
3. 1456
4. 1084

Solution: The problem clearly states that when we reduce 28, 37 and 18 rupees, respectively from Bonnie’s, Christy’s and Violet’s shares, the resultant ratio is: 4:6:9.

Thus, if we assume the reduced values as

4x, 6x and 9x, we will have –

Bonnie’s share = 4x + 28,

Christy’s share = 6x + 37 and

Violet’s share = 9x + 18 and thus we have

(4x + 28) + (6x + 37) + (9x + 18) = 5783

19x = 5783 – 83 = 5700, Hence, x = 300.

And Bonnie’s share is Rs. 1228.

Note: For problems based on ratio and proportion we are always confronted with ratios and proportions between different numbers of variables. For the above problem, we had three variables which were in the ratio of 4:6:9. When we have such a situation we normally assume the values in the same proportion, using one unknown ‘x’ only (in this example we could take the three values as 4x, 6x and 9x, respectively).

Then, the total value is represented by the addition of the three giving rise to a linear equation, which upon solving, will result in the answer to the value of the unknown ‘x’.

However, the student should realise that most of the time this unknown ‘x’ is not needed to solve the problem. This is illustrated through the following alternate approach to solving the above problem:

Assume the three values as 4, 6 and 9

Then we have

(4 + 28) + (6 + 37) + (9+ 18) = 5783

19 = 5783 – 83 = 5700 à 1 = 300

Hence, 4 + 28 = 1228.

GMAT Ratio and Proportion Problem 2:

If 10 persons can clean 10 floors by 10 mops in 10 days, in how many days can 8 persons clean 8 floors by 8 mops?

1. 12 1/2days
2. 8 days
3. 10 days
4. 8 1/3 days

Solution: For starters, do not get confused by the distractions given in the problem. 10 men and 10 days mean 100 man-days are required to clean 10 floors.

That is, 1 floor requires 10 man-days to get cleaned. Hence, 8 floors will require 80 man-days to clean.

Therefore, 10 days are required to clean 8 floors.

GMAT Ratio and Proportion Problem 3:

Three quantities A, B, C are such that AB = KC, where K is a constant. When A is kept constant, B varies directly as C; when B is kept constant, A varies directly as C and when C is kept constant, A varies inversely as B.

Initially, A was at 5 and A:B:C was 1:3:5. Find the value of A when B equals 9 at constant C.

1. 8
2. 33
3. 9
4. 5

Solution: Initial values are 5, 15 and 25. Thus we have 5 x 15 = K x 25.

Hence, K = 3.

Thus, the equation is AB = 3C.

For the problem, keep C constant at 25. Then, A x 9 = 3 x 25.

i.e ., A = 75/9 = 8.33

GMAT Ratio and Proportion Problem 4:

If x/y = 3/4, then find the value of the expression, (5x – 3y)/ (7x + 2y).

1. 3/21
2. 5/29
3. 3/29
4. 5/33

Solution: Assume the values as x = 3 and y = 4

Then we have

(15-12) / (21+8) = 3/29

GMAT Ratio and Proportion Problem 5:

The ratio of water and milk in a 30-litre mixture is 7:3. Find the quantity of water to be added to the mixture in order to make this ratio 6:1

1. 30
2. 32
3. 33
4. 35

Solution: Try and solve while reading – As you read the first sentence, you should have 21 litres of water and 9 litres of milk in your mind.

In order to get the final result, we keep the milk constant at 9 litres.

Then, we have 9 litres, which corresponds to 1

Hence, ‘?’ corresponds to 6.

Solving by using the unitary method we have:

54 litres of water to 9 litres of milk.

Hence, we need to add 33 litres of water to the original mixture, easy peasy!

Alternatively, we can solve this by using options.

GMAT Ratio and Proportion Problem 6:

Three containers A, B and C are having mixtures of milk and water in the ratio of 1:5, 3:5 and 5:7, respectively. If the capacities of the containers are in the ratio 5:4:5, find the ratio of milk to water, if the mixtures of all the three containers are mixed together.

Solution: Assume that there are 500, 400 and 500 litres respectively in the 3 containers.

Then we have 83.33, 150 and 208.33 litres of milk in each of the three containers.

Thus, the total milk is 441.66L. Hence, the amount of water in the mixture is

1400 – 441.66 = 958.33 litres

Hence, the ratio of milk to water is:

441.66 : 958.33  à  53 : 115 (Using division by 0.33333)

The calculation thought process should be:

(441 x 3 + 2) : (958 x 3 + 1) = 1325 : 2875

Dividing by 25 à 53:115

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