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Ratio Proportion - April 08, 2005

The GMAT Sample Math Practice question for the day is a ratio proportion problem.

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?

A. $495
B. $510
C. $480
D. $375
E. $360

The correct choice is (A) and the correct answer is $495.

Explanatory Answer
Let the sums of money received by A, B and C be x, y and z respectively.

Then x - 10 : y - 20 : z -15 is 11a : 18a : 24a

When $10, $20 and $15 are removed, we are removing a total of $45 from $1105.

Therefore, 11a + 18a + 24a = 1105 - 45 = 1060
i.e., 53a = 1060
or a = 20.

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

Therefore, z = 480 + 15 = $495
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