Question

Two numbers are in the ratio 3 : 5 and their sum is 96. The larger number is

(a) 36
(b) 42
(c) 60
(d) 70

Answer 1

Let the larger number be x.

Then, the smaller number be (96 − x).

According to the question,
$$\begin{gathered} \frac{96-x}{x}=\frac{3}{5} \\ \Rightarrow \frac{\left(96-x\right)\times x\times 5}{x}=\frac{3\times x\times 5}{5} \\ \Rightarrow 5\left(96-x\right)=3x \\ \Rightarrow 480-5x=3x \\ \Rightarrow 3x+5x=480 \\ \Rightarrow 8x=480 \\ \Rightarrow \frac{8x}{8}=\frac{480}{8} \\ \Rightarrow x=60 \end{gathered}$$

Thus, the larger number is 60.

Hence, the correct option is (c).