The present ages of three persons are in the proportion of 5:8:7

Question

The present ages of three persons are in the proportion of 5:8:7. Eight years ago, the sum of their ages was 76. Find the present age of the youngest person.

(A) 15 
(B) 20
(C) 25
(D) 30
(E) 32

BrentGMATPrepNow · Accepted Answer

The present ages of three persons are in the proportion of 5 : 8 : 7  
So, the three ages COULD be 5, 8 and 7
Or, the three ages COULD be 10, 16 and 14
Or, the three ages COULD be 15, 24 and 21
Or, the three ages COULD be 20, 32 and 28
.
.
.
etc.
Notice that the 3 present ages will always be multiples of 5, 8 and 7 respectively.

So, we could write.....
Let 5x = PRESENT age of youngest person
Let 8x = PRESENT age of oldest person
Let 7x = PRESENT age of middle person

Eight years ago, the sum of their ages was 76  
 Eight years ago , the ages were are follows:
5x - 8 = age of youngest person
8x - 8 = age of oldest person
7x - 8 = age of middle person

So, we can write: (5x - 8) + (8x - 8) + (7x - 8) = 76
Simplify: 20x - 24 = 76
So, 20x = 100
Solve:  x = 5

5x = PRESENT age of youngest person
So, the present age of the youngest person = 5( 5 ) = 25

Answer: C

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gracie · Answer

20x-24=76
x=5
5x=25

Abhishek009 · Answer

( 5x - 8 ) + ( 8x - 8 ) + ( 7x - 8 ) = 76

Or, 20x - 24 = 76

Or, 20x = 100

Or, x = 5

The present age of the youngest member will be 5*5 = 25 Years....
  
Thus, answer will be (C) 25 years..

tsimo1000 · Answer

i solved this question by trying the answer choices. i rewrote the ratios to be 5/20, 8/20 and 7/20. obviously the youngest is fourth of the sum of three ages. since 8 years ago their sum was 76, now their sum must be 76+ (8x3) = 100. option C is the 25% or fourth of 100. and therefore it is the correct answer.

mimajit · Answer

since 8 years ago their sum was 76, now their sum must be 76+ (8x3) = 100.

Thier present ages are in the ratio of 5:8:7 
and we know 5X + 8x+ 7x = 100
20X = 100 and X = 5

Yongest person will be 5X or 5*5 = 25 ( C)

Or

( 5x - 8 ) + ( 8x - 8 ) + ( 7x - 8 ) = 76

Or, 20x - 24 = 76

Or, 20x = 100

Or, x = 5

The present age of the youngest member will be 5*5 = 25 Years....

Kinshook · Answer

Let their present ages be 5x, 8x & 7x respectively

Sum of their ages 8 years ago = 20x - 24 = 76
20x = 100
x=5

Age of the youngest person = 5x = 25

IMO C

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ScottTargetTestPrep · Answer

We can create the equation:

5x - 8 + 8x - 8 + 7x - 8 = 76

20x = 100

x = 5

Therefore, the youngest person is currently 5(5) = 25 years old.

Answer: C

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The present ages of three persons are in the proportion of 5:8:7

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