Question

A number is divided into two parts, such that one part is 10 more than the other. If the two parts are in the ratio 5 : 3, find the number and the two parts.

• A. The number = 35 and the two parts are 15 and 20.
• B. The number = 45 and the two parts are 20 and 25.
• C. The number = 50 and the two parts are 15 and 35.
• D. The number = 40 and the two parts are 15 and 25.

Answer 1

The correct option is D

The number = 40 and the two parts are 15 and 25.

Let one part of the number be $x$

Then the other part = $x+10$

The ratio of the two numbers is 5 : 3

Therefore, $\frac{x+10}{x}=\frac{5}{3}$

⇒ $3(x+10)=5x$

⇒ $3x+30=5x$

⇒ $30=5x-3x$

⇒ $30=2x$

⇒ $x=15$

⇒ $x=15$

Therefore, $x+10=15+10=25$

The number = 25 + 15 = 40 and the two parts are 15 and 25.