Question

a man sold a book at 9% profit and a pen at 13% profit. if the sold the book at 13% profit and pen at 9% ,he gain ₹80 more.find the cost price of the book and pen if he purchase both at ₹20000.​

Answer 1

Answer:

Book=100x

Pen=100y

109x+113y-(113x+109y)=80

4y-4x=80

400y-400x=8000-----(1)

100x+100y=20000

400x+400y=80000---(2)

1)+2)=800y=88000

100y=11000

100x=9000

Step-by-step explanation:

Answer 2

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.