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

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The present ages of three persons are in the proportion of 5:8:7  [#permalink]

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New post 18 Feb 2017, 01:53
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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

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Re: The present ages of three persons are in the proportion of 5:8:7  [#permalink]

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New post 18 Feb 2017, 09:06
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saswata4s wrote:
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


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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Re: The present ages of three persons are in the proportion of 5:8:7  [#permalink]

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New post 18 Feb 2017, 14:06
saswata4s wrote:
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


20x-24=76
x=5
5x=25
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Re: The present ages of three persons are in the proportion of 5:8:7  [#permalink]

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New post 18 Feb 2017, 23:41
saswata4s wrote:
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


( 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..

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Re: The present ages of three persons are in the proportion of 5:8:7  [#permalink]

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New post 17 Apr 2019, 21:14
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.
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The present ages of three persons are in the proportion of 5:8:7  [#permalink]

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New post 04 Dec 2019, 04:53
saswata4s wrote:
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


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....
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Re: The present ages of three persons are in the proportion of 5:8:7  [#permalink]

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New post 04 Dec 2019, 10:16
saswata4s wrote:
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


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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Re: The present ages of three persons are in the proportion of 5:8:7  [#permalink]

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New post 09 Dec 2019, 18:48
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saswata4s wrote:
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


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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Re: The present ages of three persons are in the proportion of 5:8:7   [#permalink] 09 Dec 2019, 18:48
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