Question

A man buys an article for ₹ x and sells it for ₹ 56 at a gain of x%. Find the value of x.

[Hint : $$\frac{(100 + x)}{100} \times x = 56.$$]

Answer 1

Cost price ($$\text{CP}$$) $$= ₹\ x$$. 

Gain percentage $$= x%$$. 

Selling price ($$\text{SP}$$) $$= \text{CP} \times \left(\frac{100 + \text{Gain}%}{100}\right) = x \times \left(\frac{100 + x}{100}\right)$$. 

According to the problem: $$\frac{x(100 + x)}{100} = 56$$ 

$$100x + x^2 = 5600$$

$$x^2 + 100x - 5600 = 0$$ 

Factoring: $$x^2 + 140x - 40x - 5600 = 0$$ 

$$x(x + 140) - 40(x + 140) = 0$$

$$(x + 140)(x - 40) = 0$$

$$x = -140 \quad \text{or} \quad x = 40$$ 

Since cost price cannot be negative, reject $$x = -140$$. 

Hence, $$x = 40$$.