Question

A man sold one book at 9% profit and a pen 13% profit. if he sells book at 13% and pen at 9% profit then he get 80 rupees more. find the cost price of book and pen if he purchase both in 20,000​

Answer 1

Answer:

Cost price of the book = 11000 Rs.

Cost price of the pen = 9000 Rs.

Step-by-step explanation:

Let the price of the book is x and the price of the pen is y

Then

$x+y=20000$        ...............(1)

Selling price of book at 9% profit

$=x+\frac{9x}{100}$

$=x+0.09x$

$=1.09x$

Selling price of book at 13% profit

$=x+\frac{13x}{100}$

$=x+0.13x$

$=1.13x$

Similary

Selling price of pen at 13% profit

$=y+\frac{13y}{100}$

$=y+0.13y$

$=1.13y$

And, Selling price of pen at 9% profit

$=1.09y$

According to the question

$(1.13x+1.09y)-(1.09x+1.13y)=80$

$\implies 0.04x-0.04y=80$

$\implies 0.01x-0.01y=20$

$\implies x-y=2000$        ...............(2)

Adding eq (1) and (2)

$2x=22000$

$\implies x=11000$

Therefore,

$y=20000-11000$

$y=9000$

Therefore,

Cost price of the book = 11000 Rs.

Cost price of the pen = 9000 Rs.

Hope this helps.

Answer 2

Answer:

Cost Price of Book = Rs. 11,000

Cost Price of Pen = Rs. 9,000

Step-by-step explanation:

In the question,

Let us say that the Cost Price, CP of Book = x

and,

Cost Price of Pen = y

So,

Case 1 :

Book sold at profit = 9 %

Pen sold at profit = 13%

So,

Selling Price of Book, SP is,

$SP=x+\frac{9}{100}(x)=1.09x$

Selling Price of Pen is,

$SP=y+\frac{13}{100}(y)=1.13y$

Case 2 :

Book sold at profit = 13 %

Pen sold at profit = 9%

Profit made = 80 Rs.

So,

Selling Price of Book, SP is,

$SP=x+\frac{13}{100}(x)=1.13x$

Selling Price of Pen is,

$SP=y+\frac{9}{100}(y)=1.09y$

Now,

Also,

Cost price of Book and Pen both is Rs. 20,000.

So,

$x + y = 20000 ..........(1)$

Now,

From Case 1 and 2 we can say that,

$(1.09x+1.13y)=(1.13x+1.09y)-80\\0.04x-80=0.04y\\0.04x-0.04y=80\\x-y=2000 ........(2)$

On adding eqn. (1) and (2) we get,

$2x=22,000\\x=11,000\\and,\\y=9,000$

Therefore,

Cost Price of Book = Rs. 11,000

Cost Price of Pen = Rs. 9,000