JIPMAT 2022 (QA) - Three years ago, the ratio of ages of Amisha and Namisha was 8:9. Three years from now the ratio will become 11:12. What is the present age of Amisha? | PYQs + Solutions

JIPMAT 2022

Arithmetic

Ratio, Proportion & Variation

Medium

Three years ago, the ratio of ages of Amisha and Namisha was 8:9. Three years from now the ratio will become 11:12. What is the present age of Amisha?

2 years

16 years

19 years

21 years

Correct Option: 3

Let present age of Amisha =

x

years

\newline

Then present age of Namisha =

y

years

Three years ago:

\newline

(x-3):(y-3) = 8:9

9(x-3) = 8(y-3)

...(1)

Three years later:

\newline

(x+3):(y+3) = 11:12

12(x+3) = 11(y+3)

...(2)

From (1):

\newline

9x - 27 = 8y - 24

9x - 8y = 3

...(3)

From (2):

\newline

12x + 36 = 11y + 33

12x - 11y = -3

...(4)

Subtracting (4) from (3):

\newline

-3x + 3y = 6

x - y = -2

Substituting in (3):

\newline

9x - 8(x+2) = 3

9x - 8x - 16 = 3

x - 16 = 3

x = 19

Therefore, Amisha's present age is 19 years.