# GMAT Quant : Ratio Proportion

Concept: Ratio Proportion

The GMAT Sample Math Practice question is a ratio proportion problem on dividing a sum of money among 3 people.

#### Question: Three friends Alice, Bond and Charlie divide \$1105 amongst them in such a way that if \$10, \$20 and \$15 are removed from the sums that Alice, Bond and Charlie received respectively, then the share of the sums that they got will be in the ratio of 11 : 18 : 24. How much did Charlie receive?

1. \$495
2. \$510
3. \$480
4. \$375
5. \$360

Video explanation will be added soon.

Let the amount of money received by A, B and C be x, y and z respectively.
Sum of money with the three of them, x + y + z = 1105.
It is mentioned that the money that they possess are in the ratio 11:18:24, after removing \$10, \$20 and \$15 respectively.
Then x - 10 : y - 20 : z -15 will be in the ratio 11 : 18 : 24

So, x – 10 = 11k, y – 20 = 18k and z – 15 = 24k
Adding the money left with the three of them after removing \$10, \$20 and \$15 respectively, we get
x – 10 + y – 20 + z – 15 = 11k + 18k + 24k
Or x + y + z – 10 – 20 – 15 = 53k
Or x + y + z – 45 = 53k
We know x + y + z = 1105.
So, 1105 – 45 = 53k
1060 = 53k
or k = 20.

To compute the amount that C received, substitute value of k in ratio of z.

We know that z - 15 = 24k
z - 15 = 24 * 20 = 480

Therefore, z = 480 + 15 = \$495 