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