Banking Quantitative Aptitude Sample Paper Quantitative Aptitude Sample Paper-3

The ratio of the present ages of Sushma and Karishma is 6: 7 respectively. The ratio of their ages 8 yr hence would be 8: 9 respectively. What would be the respective ratio of their ages after 12 yr? [NICL (AO) 2015]

A) 17: 19

B) 15: 17

C) 9: 10

D) 10: 11

E) None of these

Correct Answer: C

Solution :

[c] Let the present ages of Sushma and Karishma be s and k, respectively.

According to the question,

\[\frac{s}{k}=\frac{6}{7}\]\[\Rightarrow \]\[7s=6k\] (i)

and \[\frac{s+8}{k+8}=\frac{8}{9}\]

\[\Rightarrow \] \[9s+72=8k+64\]\[\Rightarrow \]\[8k-9s=8\]

\[\Rightarrow \] \[8\times \frac{7}{6}s-9s=8\] [using Eq. (i)]

\[\Rightarrow \] \[\frac{28s}{3}-9s=8\]\[\Rightarrow \]\[28s-27s=24\]

\[\Rightarrow \] \[s=24\]

And therefore \[k=\frac{7s}{6}=28\]

Hence, \[\frac{s+12}{k+12}=\frac{24+12}{28+12}=\frac{36}{40}=\frac{9}{10}\]