Question

The price of a radio was increased by 25 percent. The new price was then increased by 40 percent. A single increase of what percent is equivalent to these two successive increases?

A. 80%
B. 75%
C. 65%
D. 50%
E. 45%

Answer 1

The correct option is B. 75%

Step-by-step explanation:

Suppose x be the original price of the radio,

After increasing the price by 25%,

New price = x + 25% of x

`=x + (25x)/(100)`

`=x +(x)/(4)`

`=(4x+x)/(4)`

`=(5x)/(4)`

Again after increasing by 40%,

Final price =
`(5x)/(4)+40\%\text{ of }(5x)/(4)`

`=(5x)/(4)+(5x* 40)/(400)`

`=(5x)/(4)+(x)/(2)`

`=(5x + 2x)/(4)`

`=(7x)/(4)`

Hence, the total increment percentage in price

`=\frac{\text{Final price-Original price}}{\text{Original price}}* 100`

`=((7x)/(4)-x)/(x)* 100`

`=(7x-4x)/(4x)* 100`

`=(3)/(4)* 100`

`=3* 25`

= 75%

i.e. OPTION B is correct.