Question

If a discount of 10 percent be given on marked price of the book, the published gains 20 percent. If the discount is increased to 15 percent, what will be the gain percent.

Answer 1

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$\underline{\underline{\large{\textbf{Solution:}}}}$
Given,
A discount of 10% be given on marked price of the book, Publisher Gains 20%

If the discount is increased to 15%, Gain% = ?

$\underline{\large{\textbf{Step-1}}}$:
Find the Selling Price of the Book, when discount = 10%.

$Selling\: Price (SP) = Marked\: Price - [Discount \% \times Marked\: Price]$

$Selling\: Price (SP) = Marked\: Price[1 - Discount\%]$

Let Marked Price of the book = 100

Substituting Values

$\implies SP = 100[1-(\frac{10}{100})]$

$\implies SP = 100[1-(\frac{1}{10})]$

$\implies SP = 100(\frac{9}{10})$

$\implies SP = 90$

Selling Price = 90.

$\underline{\large{\textbf{Step-2}}}$:
Find the Cost Price of the Book

We have,
$Selling\: Price (SP) = \dfrac{100+Gain\%}{100}\times Cost\: Price(CP)$

$\implies CP = \dfrac{SP}{(\frac{100+Gain\%}{100})}$

Substituting Values

$\implies CP = \dfrac{90}{(\frac{100+20}{100})}$

$\implies CP = \dfrac{900}{12}$

$\implies CP =75$

$\underline{\large{\textbf{Step-3}}}$:
Find the Selling Price when discount = 15%

Substituting Values

$\implies SP = 100[1-(\frac{15}{100})]$

$\implies SP = 100(\frac{100-15}{100})$

$\implies SP = 100(\frac{85}{100})$

$\implies SP = 85$

$\underline{\large{\textbf{Step-3}}}$:
Find the Gain earned by the publisher

$Gain = Selling\: Price(SP) - Cost\: Price(CP)$

Substituting Values

$\implies Gain = 85 - 75$

$\implies Gain = 10$

$\underline{\large{\textbf{Step-4}}}$:
Find the Gain% when Discount is changed from 10% to 15%

$Gain\% = \dfrac{Gain \times 100}{CP}$

Substituting Values

$\implies Gain \% = \dfrac{100 \times 10}{75}$

$\implies Gain \% = \dfrac{1000}{75}$

$\implies Gain \% = \dfrac{1000}{75}$

$\implies Gain \% = \dfrac{40}{3}\%$

$\implies Gain \% =13 \, \frac{1}{3}\%$

$\implies Gain \% = 13.33\%$

Therefore,
Gain Percent = 13.33%

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