Three years back, a father was 24 years older than his son. At present : Problem Solving (PS)

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Three years back, a father was 24 years older than his son. At present

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Math Expert

Joined: 02 Sep 2009

Posts: 60647

Three years back, a father was 24 years older than his son. At present [#permalink]

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14 Feb 2016, 05:30

00:00

Difficulty:

35% (medium)

Question Stats:

79% (01:43) correct

21% (01:27) wrong

based on 20 sessions

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Three years back, a father was 24 years older than his son. At present the father is 5 times as old as the son. How old will the son be three years from now?

A. 12 years
B. 6 years
C. 3 years
D. 9 years
E. 27 years

Spoiler: OA

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Intern

Joined: 23 Dec 2015

Posts: 3

Three years back, a father was 24 years older than his son. At present [#permalink]

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14 Feb 2016, 08:42

According to the statement, 3 years back the father was 24 years older than his son.
Mathematically we can write it like that :

(Y-3)-(X-3) = 24

Now the faher is 5 time older than his son, again we can write it like that :

5x = Y

thats give us a system of linear equation

(Y-3) - ( X - 3) = 24
5X = Y

Where Y is the age of the father and X the age of the son nowadays.

According to this we can easily solve the system by remplacing the Y in the first equation by the 5X in the second equation :

5X -3 - (x - 3) = 24
X= 6

According to X equal 6 we can conclude that X + 3 is the age of the son 3 years from now.

Intern

Joined: 14 Dec 2014

Posts: 18

Concentration: Technology

Re: Three years back, a father was 24 years older than his son. At present [#permalink]

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14 Feb 2016, 10:12

Using linear equations to convert the word problem:
** F = fathers current age & S = sons current age

#1 Three years back, a father was 24 years older than his son: F-3 = 24 + (S - 3)
#2 At present the father is 5 times as old as the son: F = 5*S

How old will the son be three years from now?: S + 3 = ?
With two variables and two linear equations we are able to solve the problem:

(S*5) - 3 = 24 +S -3
4S=24
S = 6

S + 3 = 6 + 3 = 9

Answer: D