Question

a man sold a book at a loss of 20%. if he had sold the book 12 rupees more he would have gained 10%. find the cost price of the book.​

Answer 1

The answer will be 40 .

I HOPE IT HELPS .

Answer 2

GivEn :

• SP (Loss %) = 20 %

• If he had sold the book at Rs 12 then he would have gained 10 %.

To find :

• Cost price of the book = ?

Formula usEd :

To solve this question you need to know the imp. formulas related to SP and CP !!

$\bullet\large \: { \boxed{ \sf{\: SP = \dfrac{100 - L \: \% }{100} \times CP}}}$

$\bullet\large \: { \boxed{ \sf{\: SP = \dfrac{100 + G \: \%}{100} \times CP }}}$

Here,

• G% = Gain Percentage

• L% = Loss Percentage

• CP = Cost Price

• SP = Selling Price

Let's proceed to the question now !!

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SoluTion :

Let us assume that x be the Cost Price of the book,

According to Selling Price formula ,

$:\implies \sf \: \: \: SP = \dfrac{100 - L \: \% }{100} \times CP$

$:\implies \sf \: \: \: SP = \dfrac{100 - 20 \: \% }{100} \times x$

$:\implies \sf \: \: \: SP = \dfrac{80 }{100} \times x$

$:\implies \sf \: \: \: SP = 0.8 x$

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As it is given that, if he had sold the book at Rs 12 then he would have gained 10 %.

So,

$: \implies \sf \: \: \: \dfrac{100 + G \: \%}{100} \times CP = 0.8x + 12$

$: \implies \sf \: \: \: \dfrac{100 + 10}{100} \times x = 0.8x + 12$

$: \implies \sf \: \: \: \dfrac{110}{100} \times x = 0.8x + 12$

$: \implies \sf \: \: \: 1.1 \times x = 0.8x + 12$

$: \implies \sf \: \: \: 12 = 1.1x - 0.8x$

$: \implies \sf \: \: \: 12 = 0.3x$

$: \implies \sf \: \: \: x = \dfrac{12}{0.3}$

$: \implies \sf \: \: \: { \underline{ \boxed{ \sf{ \purple{ Rs \: x = 40}}}}} \: \bigstar$

Therefore, the Cost Price(CP) of the book is Rs 40 .

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