Question

A. man sold. a book. at. a loss. of. 20% If he. had. sold. for. rs 12 more he. would. have. gained. 10% find. the. cost. prive of. the. book . please. send. this. answer. fastly​

Answer 1

Answer:-

Let the CP of the book be Rs. x.

Given that,

The book was sold at a loss of 20%.

We know,

SP = CP × (100 - loss%)/100

So,

⟹ SP of book = x * (100 - 20)/100

⟹ SP of book = x * 80/100

⟹ SP of book = Rs. 80x/100

Also given that,

If the book is sold for Rs. 12 more, a gain of 10% would be occured.

Now,

• New SP of the book = Rs. (80x/100 + 12)
• Gain% = 10%.

We know,

CP = SP * 100/ (100 + gain%)

⟹ x = {(80x/100 + 12) * 100 } / (100 + 10)

⟹ x = (80x + 1200)/110

⟹ 110x = 80x + 1200

⟹ 110x - 80x = 1200

⟹ 30x = 1200

⟹ x = 1200/30

⟹ x = Rs. 40

∴ The cost price of the book is Rs. 40.

Answer 2

Given :

• Man sold a book at loss = 20%
• If he had sold book for Rs. 12 more he would have gain = 10%

To Find :

• Cost price of the book?

Formula used :

$\star\:\large{\boxed{\bf{SP = \dfrac{100 - Loss\%}{100}\:\times\:CP}}}$

$\star\:\large{\boxed{\bf{SP = \dfrac{100 + Gain\%}{100}\:\times\:CP}}}$

Solution :

• Let cost price of book (CP) be y

According to first case he sold a book at 20% loss. Therefore, by putting all values im formula we get,

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

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

$\\ :\implies\:\sf SP = 0.8\:\times\:y$

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

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Now, we know that if he had sold book for Rs. 12 more he would have 10% gain. Therefore, by putting all values im formula we get,

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

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

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

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

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

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

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

$\\ :\implies\:\sf y = \dfrac{12\:\times\:10}{3}$

$\\ :\implies\:\sf y = {\cancel{\dfrac{120}{3}}}$

$\\ :\implies\:\large{\underline{\boxed{\bf{y = 40}}}}$

Hence, cost price of book is Rs. 40.

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Important Formulae :

$\pink{\bigstar}$ $\sf Gain\:\leadsto\:\boxed{\bf{\blue{SP - CP}}}$

$\pink{\bigstar}$ $\sf Loss\:\leadsto\:\boxed{\bf{\blue{CP - SP}}}$

$\pink{\bigstar}$ $\sf Gain\%\:\leadsto\:\boxed{\bf{\blue{ \dfrac{Gain\:\times\:100}{CP}}}}$

$\pink{\bigstar}$ $\sf Loss\%\:\leadsto\:\boxed{\bf{\blue{ \dfrac{Loss\:\times\:100}{CP}}}}$

$\pink{\bigstar}$ $\sf SP\:\leadsto\:\boxed{\bf{\blue{\bigg\lgroup \dfrac{100 + Gain\%}{100}\bigg\rgroup\:\times\:CP}}}$

$\pink{\bigstar}$ $\sf SP\:\leadsto\:\boxed{\bf{\blue{\bigg\lgroup \dfrac{100 - Loss\%}{100}\bigg\rgroup\:\times\:CP}}}$

$\pink{\bigstar}$ $\sf CP\:\leadsto\:\boxed{\bf{\blue{\bigg\lgroup \dfrac{100}{100 + Gain\%}\bigg\rgroup\:\times\:SP}}}$

$\pink{\bigstar}$ $\sf CP\:\leadsto\:\boxed{\bf{\blue{\bigg\lgroup \dfrac{100}{100 - Loss\%}\bigg\rgroup\:\times\:SP}}}$

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