Question

A shopkeeper buys x books for ₹ 720.

1. Write the cost of 1 book in terms of x. 
2. If the cost per book be ₹ 5 less, the number of books that could be bought for ₹ 720 would be 2 more. 

Write down the equation in x and solve it to find x.

Answer 1

i. Cost of 1 book $$= ₹\ \frac{720}{x}$$.

ii. If the cost per book is ₹ 5 less, new cost per book $$= ₹\ \left(\frac{720}{x} - 5\right)$$. 

At this cost, $$(x + 2)$$ books can be bought for ₹ 720, so cost of 1 book is also $$₹\ \frac{720}{x + 2}$$.

Therefore: $$\frac{720}{x} - \frac{720}{x + 2} = 5$$ 

Dividing throughout by 5: $$\frac{144}{x} - \frac{144}{x + 2} = 1$$

$$144\left(\frac{x + 2 - x}{x(x + 2)}\right) = 1$$

$$\frac{288}{x^2 + 2x} = 1$$

$$x^2 + 2x - 288 = 0$$ 

Factoring: $$(x + 18)(x - 16) = 0$$

$$x = -18 \quad \text{or} \quad x = 16$$ 

Since number of books cannot be negative, reject $$x = -18$$.

Hence, $$x = 16$$.