Question

Find the Cost price when : S.P. = rs 1500 and gain = 20%

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Answer 1

Given :

• Selling price (SP) = Rs.1500
• Gain% = 20%

To Find :

• Cost price (CP)

Solution :

The relation between Cost price (CP) , Selling price (SP) & Gain% is ,

$\\ {\boxed{\bf{Gain\% = \frac{( SP-CP )}{CP} \times 100 }}}$

We have ,

• SP = Rs.1500
• Gain% = 20%

Substituting the values in the formula ,

$\\ : \implies \sf 20 = \dfrac{(1500 -CP )}{CP} \times 100$

$\\ : \implies \sf 20CP= (1500 - CP)100$

$\\ : \implies \sf 20CP = 1500(100) - 100CP$

$\\ : \implies \sf \: 20CP + 100CP = 1500 \times 100$

$\\ : \implies \sf \: 120CP = 1500 \times 100$

$\\ : \implies \sf \:CP = \frac{1500 \times 100}{120}$

$\\ : \implies \boxed{\bf{{ CP= \: Rs.1250}}} \: \dag$

∴ The cost price (CP) is Rs.1250

Answer 2

Answer:

Given :-

• Selling Price is Rs 1500 and gain percentage is 20%.

To Find :-

• What is the cost price.

Formula Used :-

$\clubsuit$ Profit or Gain Percentage Formula :

$\footnotesize\mapsto \sf\boxed{\bold{\pink{Gain\% =\: \bigg\lgroup\dfrac{Selling\: Price - Cost\: Price}{Cost\: Price}\bigg\rgroup \times 100}}}$

Solution :-

Let,

$\mapsto \sf\bold{\purple{Cost\: Price =\: Rs\: x}}$

Given :

$\bigstar\: \: \bf{Selling\: Price =\: Rs\: 1500}$

$\bigstar\: \: \bf{Gain\% =\: 20\%}$

According to the question by using the formula we get,

$\longrightarrow \sf 20 =\: \dfrac{1500 - x}{x} \times 100$

$\longrightarrow \sf 20 =\: \dfrac{(1500 - x) \times 100}{x}$

$\longrightarrow \sf 20 =\: \dfrac{150000 - 100x}{x}$

By doing cross multiplication we get,

$\longrightarrow \sf 20x =\: 150000 - 100x$

$\longrightarrow \sf 20x + 100x =\: 150000$

$\longrightarrow \sf 120x =\: 150000$

$\longrightarrow \sf x =\: \dfrac{15000\cancel{0}}{12\cancel{0}}$

$\longrightarrow \sf x =\: \dfrac{\cancel{15000}}{\cancel{12}}$

$\longrightarrow \sf x =\: \dfrac{1250}{1}$

$\longrightarrow \sf\bold{\red{x =\: Rs\: 1250}}$

${\small{\bold{\underline{\therefore\: The\: cost\: price\: is\: Rs\: 1250\: .}}}}$

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EXTRA INFORMATION :-

❒ $\sf \bold{\pink{Profit =\: SP - CP}}$

❒ $\sf \bold{\pink{Loss =\: CP - SP}}$

❒ $\sf\bold{\pink{CP =\: \bigg(\dfrac{100}{100 + Gain\%}\bigg) \times SP}}$

❒ $\sf\bold{\pink{CP =\: \bigg(\dfrac{100}{100 - Loss\%}\bigg) \times SP}}$

❒ $\sf\bold{\pink{SP =\: \bigg(\dfrac{100 + Gain\%}{100}\bigg) \times CP}}$

❒ $\sf\bold{\pink{SP =\: \bigg(\dfrac{100 - Loss\%}{100}\bigg) \times CP}}$