Question

A women bought a certain number of books for Rs. $200$. She kept one for her own and sold the rest at the rate Rs. $40$ more than she gave for one book. Besides getting her own book for nothing, she made a profit of Rs. $100$. How many books did she buy?

• A. $10$
• B. $20$
• C. $30$
• D. $40$

Answer 1

Answer: (A)

$10$

$n=$ number of books purchased
$p=$ price paid per book
$np=200$, so $p=$ $\frac{200}{n}$
$(n-5)(p+40)=300$ (As per the statement given)
$np+40n-5p-200=300$
$200+40n-\frac{1000}{n}-200-300=0$
$40n^2-300n-1000=0$
On factoring, we get
$(n-10)(n+2.5)=0$
$n=10$ or $-2.5$
Answer cannot be negative.
So, number of books $=10$.