IPMAT Rohtak 2019 (QA) - John's present age is one fourth of his father's age two years ago. John's father's age will be twice Raman's age after 10 years. If Raman's 12th birthday was celebrated 2 years ago, then what is John's present age? | PYQs + Solutions

IPMAT Rohtak 2019

Algebra

Linear Equation

Medium

John's present age is one fourth of his father's age two years ago. John's father's age will be twice Raman's age after 10 years. If Raman's 12th birthday was celebrated 2 years ago, then what is John's present age?

5 years

7 years

9 years

11 years

Correct Option: 3

Let John's present age be

x

years

Given:

\newline

x = \frac{1}{4}

of father's age 2 years ago

\newline

Father's age after 10 years = 2 × Raman's age after 10 years

\newline

Raman's age now =

12 + 2 = 14

years

Let's solve:

\newline

If John's father's age now is

y

years

\newline

His age 2 years ago was

(y-2)

years

Therefore:

x = \frac{y-2}{4}

... (1)

After 10 years:

\newline

Raman's age =

14 + 10 = 24

years

\newline

Father's age =

y + 10

years

Given:

y + 10 = 2 \times 24

\newline

y + 10 = 48

\newline

y = 38

years

Substituting in equation (1):

\newline

x = \frac{38-2}{4} = \frac{36}{4} = 9

Therefore, John's present age is

9

years.