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%

Question

contestada

Respuesta :

slicergiza slicergiza · Answer 1 · 2019-12-11T06:51:21+01:00

Answer:

The correct option is B. 75%

Explanation:

Suppose x be the original price of the radio,

After increasing the price by 25%,

New price = x + 25% of x

[tex]=x + \frac{25x}{100}[/tex]

[tex]=x +\frac{x}{4}[/tex]

[tex]=\frac{4x+x}{4}[/tex]

[tex]=\frac{5x}{4}[/tex]

Again after increasing by 40%,

Final price = [tex]\frac{5x}{4}+40\%\text{ of }\frac{5x}{4}[/tex]

[tex]=\frac{5x}{4}+\frac{5x\times 40}{400}[/tex]

[tex]=\frac{5x}{4}+\frac{x}{2}[/tex]

[tex]=\frac{5x + 2x}{4}[/tex]

[tex]=\frac{7x}{4}[/tex]

Hence, the total increment percentage in price

[tex]=\frac{\text{Final price-Original price}}{\text{Original price}}\times 100[/tex]

[tex]=\frac{\frac{7x}{4}-x}{x}\times 100[/tex]

[tex]=\frac{7x-4x}{4x}\times 100[/tex]

[tex]=\frac{3}{4}\times 100[/tex]

[tex]=3\times 25[/tex]

= 75%

i.e. OPTION B is correct.