David and his wife each receives an 8 percent annual rise. If David receives a raise of ₹ 800 and his wife receives a raise of ₹ 840, what is the difference between their annual incomes after their raises?
(a)₹ 40
(b)₹ 460
(c)₹ 500
(d)₹ 540
Answer
Answer (as printed): D
Explanation
Let David's annual income be ₹ $x$ and his wife's annual income be ₹ $y$. Then, $8 \%$ of $x=800 \Rightarrow \frac{8}{100} x=800$ $$\Rightarrow \quad x=\left(\frac{800 \times 100}{8}\right)=10000 .$$ And, $8 \%$ of $y=840 \Rightarrow \frac{8}{100} y=840$ $$\Rightarrow \quad y=\left(\frac{840 \times 100}{8}\right)=10500 .$$ ∴ Required difference $=₹[(10500+840)-(10000+800)]$ $$=₹(11340-10800)=₹ 540 .$$
Explanation as extracted from the printed page; notation may be imperfect.