The given question is a GMAT 650 level problem solving question from the topic Ratio & Proportions. This GMAT sample question is a word problem that tests the concept of dividing a number into 3 parts based on information about the ratio in which the number has to be divided.
Question 1: Three friends Alice, Bond, and Charlie divide $1105 among 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 11 : 18 : 24. How much did Charlie receive?
Let the amount of money received by Alice, Bond and Charlie be A, B, and C respectively.
Sum of money with the three of them, A + B + C = 1105.
After removing $10, $20, and $15 from A, B, and C respectively the sum of money they have will be (A – 10), (B - 20), and (C - 15).
(A – 10) : (B - 20) : (C - 15) = 11 : 18 : 24
Let A − 10 = 11k, B − 20 = 18k and C − 15 = 24k
Adding the money left with the three of them after removing $10, $20 and $15 respectively, we get
A – 10 + B – 20 + C – 15 = 11k + 18k + 24k
A + B + C – 10 – 20 – 15 = 53k
A + B + C – 45 = 53k
From the question stem, we know that A + B + C = 1105
So, 1105 – 45 = 53k
1060 = 53k
k = 20
Substituting value of k in the ratio C - 15 = 24k,
C − 15 = 24 × 20 = 480
C = 480 + 15 = $495
Charlie received 495$
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