Question

The age of Sulekha and Arunima are in the ratio \[9:8\] respectively. After 5 years, the ratio of their ages will be \[10:9\]. What is the difference between their ages?
A. 4 years
B. 5 years
C. 6 years
D. 7 years

Answer 1

Hint: First of all, consider the ages of Sulekha and Arunima as variable. Then will obtain two equations in terms of the considered variables from the given conditions. Subtract both the equations to get the required answer.

Complete step-by-step answer:
Let the present ages of Sulekha and Arunima be \[x{\text{ and }}y\] respectively.
As the age of Sulekha and Arunima are in the ratio \[9:8\] respectively, we have
\[
   \Rightarrow \dfrac{x}{y} = \dfrac{9}{8} \\
   \Rightarrow 8x = 9y \\
  \therefore 8x - 9y = 0............................\left( 1 \right) \\
\]
After 5 years, the ratio of their ages will be \[10:9\]. So, we have
\[
   \Rightarrow \dfrac{{x + 5}}{{y + 5}} = \dfrac{{10}}{9} \\
   \Rightarrow 9\left( {x + 5} \right) = 10\left( {y + 5} \right) \\
   \Rightarrow 9x + 45 = 10y + 50 \\
   \Rightarrow 9x - 10y = 50 - 45 \\
  \therefore 9x - 10y = 5................................\left( 2 \right) \\
\]
Subtracting equation (2) from (1), we get
\[
   \Rightarrow \left( {9x - 10y} \right) - \left( {8x - 9y} \right) = 5 - 0 \\
   \Rightarrow 9x - 10y - 8x + 9y = 5 \\
   \Rightarrow x\left( {9 - 8} \right) - y\left( {9 - 8} \right) = 5 \\
  \therefore x - y = 5 \\
\]
Hence the difference between their ages \[x - y = 5{\text{ years}}\]
Thus, the correct option is B. 5 years

Note: By the solution we can say that Sulekha is older than Arunima by 5 years. By solving equations (1) and (2) we get the present ages of Sulekha and Arunima if required.