Question

successive discount of 20% and 25% are equivalent to a single discount of

A) 33%
B) 40%
C) 35%
D) 45%

​

Answer 1

Consider the original price as x,

After allowing 20% discount,

The price will now be,

⇒ x - 20% of x

⇒ 80% of x

⇒ 80/100 * x

⇒ 0.8 x

Now The price is 0.8x,

Another discount of 25% is allowed,

The price will now be,

⇒ 0.8x - 25% of ( 0.8x)

⇒ 0.8 x - 0.2 x

⇒ 0.6 x

⇒ 60% of x

The original cost was x

Cost after two successive discounts = 0.6 x

⇒Total discount = x - 0.6x

⇒ Total discount = 0.4 x

⇒ Total discount = 40% of x

Therefore, Two successive discounts of 20% and 25% are equivalent to a single discount of 40%

Required Option is B

Answer 2

Question :

The successive discount of 20% and 25% are equivalent to a single discount of

A) 33%

B) 40%

C) 35%

D) 45%

Solution :

$\underline{\bold {Given:}}$

• Successive discounts are 20% and 25%.

$\underline{\bold {To\:Find:}}$

• Single discount .

Let the original price be Rs 100.

$\implies First \: discount =Rs\: (20\% \: of \: 100 )\\ \implies First \: discount = Rs\:(\frac{20}{100} \times 100) \\ \implies First \: discount = Rs \: 20$

$\implies Price \: after \: first \: discount =Rs \:(100 - 20) \\ \implies Price \: after \: first\: discount =Rs \:80$

$\implies Second \:discount = Rs \:(25\% \: of \: 80) \\\implies Second \: discount = Rs \:( \frac{25}{100} \times 80) \\ \implies Second \: discount = Rs \:20$

$\implies Price \: after \: second \: discount =Rs \:(80 - 20) \\ \implies Price \: after \: second\: discount =Rs \:60$

Net price = Rs 60

$\implies Single\: discount = Rs \:(100-60)\\\implies Single \:discount = Rs \:40$

$\implies Single\: discount =( \frac {Single\: discount}{Original\:price}\times 100)\%\\\implies Single\: discount =(\frac{40}{100}\times 100)\%\\\implies Single \:discount=40\%$

$\boxed{\green{\therefore{Single \:discount\:equivalent \:to\: 20\% and\:25\%\:is \:40\%.}}}$