Question

A number is divided into two parts such that one part is 20 more that the others. If the two parts are in the ratio 5:3, then find the number and the two parts.

• A. The number is 80 and two parts are 30 and 50.
• B. The number is 60 and two parts are 20 and 40.
• C. The number is 70 and two parts are 25 and 45.
• D. The number is 100 and two parts are 40 and 60.

Answer 1

The correct option is A The number is 80 and two parts are 30 and 50.

Let one part of the number is $x$.
The another part is then $(x+20)$.

Now, this two numbers are in ratio 5:3.
So, $\frac{x+20}{x}=\frac{5}{3}$
$3\times (x+20)=5\times x$
$3x+60=5x$
$5x-3x=60$
$2x=60$
$x=\frac{60}{2}=30$

Hence, one part is 30 and other part is $x+20=30+20=50$.

The number is then 30 + 50 = 80.