Question

A shopkeeper buys a number of books for Rs. $80$. If he had bought $4$ more for the same amount, each book would have cost Re. $1$ less. How many books did he buy?

• A. $8$
• B. $16$
• C. $24$
• D. $28$

Answer 1

Answer: (B)

$16$

Let the total number of books be $x$.

Hence applying the above condition, we get

$\frac{80}{x}-1=\frac{80}{x+4}$

$80(\frac{1}{x}-\frac{1}{x+4})=1$

$\frac{4.\left(80\right)}{x^2+4x}=1$

$320=x^2+4x$

$(x+2{)}^2-4=320$

$(x+2{)}^2=324$

$x+2=18$ ...since price cannot be negative.

Hence, $x=16$

Thus the total number of books will be $16$.