Question

₹ 6400 were divided equally among x persons. Had this money been divided equally among (x + 14) persons, each would have got ₹ 28 less. Find the value of x.

Answer 1

Share per person originally $$= ₹\ \frac{6400}{x}$$.

Share per person for $$(x + 14)$$ persons $$= ₹\ \frac{6400}{x + 14}$$.

Given difference $$= ₹\ 28$$: $$\frac{6400}{x} - \frac{6400}{x + 14} = 28$$

Dividing by 4: $$\frac{1600}{x} - \frac{1600}{x + 14} = 7$$

$$1600\left(\frac{x + 14 - x}{x(x + 14)}\right) = 7$$

$$\frac{1600 \times 14}{x^2 + 14x} = 7$$

$$x^2 + 14x = 3200$$

$$x^2 + 14x - 3200 = 0$$ 

Factoring: $$(x + 64)(x - 50) = 0$$ 

Since number of persons cannot be negative, $$x = 50$$.