Question

A person sold a book at 20% profit. If he had bought it

at 10% less cost and sold for Rs 90 more then he

would have gained 40% profit. Find cost price of

book​

Answer 1

Answer:

Rs 1500

Step-by-step explanation:

Let the original cost price be 'x'. It is sold at a profit of 20%, so

selling price = x(1 + r/100)

                    = x(1 + 20/100)

                    = (12x/10)

If he had bought it  at 10% less cost and sold for Rs 90 more, the gain would have been 40%:

CP = x - 10% of x = x(1 - 10/100) = 9x/10

;SP = (12x/10) + 90   ; gain = 40%

         Using, gain% = (SP - CP)/CP * 100%

⇒ 40% = ((12x/10)+90 - 9x/10)/(9x/10) * 100%

⇒ 40(9x/10) = (3x/10 + 90) * 100

⇒ 36x = 30x + 9000

⇒ 36x - 30x = 9000

⇒ 6x = 9000

⇒ x = 1500

Answer 2

Question :

A person sold a book at 20% profit. If he had bought it at 10% less cost and sold for Rs 90 more then he would have gained 40% profit. Find cost price of book.

Let us assume :

The cost price of the book be ₹ x

Solution :

According to the question we know that :

Selling price has 20 % profit

Hence, formula to get it is :

$\sf \leadsto SP = CP(1 + \frac{20}{100} )$

$\sf \leadsto SP = x (1 + \frac{1}{5} )$

$\sf \leadsto SP = \frac{6x}{5}$

Now new CP,

He bought at 10 % loss and sold for ₹ 90

$\sf \looparrowright New \: CP = x(1 - \frac{10}{100} )$

$\sf \looparrowright New \: CP = x(1 - \frac{1}{10} )$

$\underline{\boxed{\sf \looparrowright CP = \frac{9x}{10} }}$

New SP

$\sf \rarr SP = \frac{6x}{5} + 90$

$\sf \rarr SP = \frac{6x \times 2}{5 \times 2} + \frac{900}{10}$

$\underline{\boxed{ \sf \rarr SP = \frac{12x+900}{10} }}$

Now,

According to the question

$\sf \mapsto \frac{9x}{10} \times \frac{140}{100} = \frac{12x + 900}{10}$

$\sf \mapsto \frac{126x}{100} = \frac{12x + 900}{10}$

By cross multiplying we get

$\sf \mapsto1260x = 1200x + 90000$

Transposing 1200x on the left hand side we get

$\sf \mapsto1260x - 1200x = 90000$

$\sf \mapsto60x = 90000$

$\sf \mapsto x = \frac{90000}{60}$

$\sf \mapsto x= 1500$

• The cost price of the book is ₹ 1500