A man buys a certain number of articles at 15 for ₹ 112.50 and sells them at 12 for ₹ 108. Find :

(i) his gain as percent;

(ii) the number of articles sold to make a profit of ₹ 75.

(i) C.P. of 15 articles = ₹ 112.50

C.P. of 1 article = ₹ $\dfrac{112.50}{15}$ = ₹ 7.5

S.P. of 12 articles = ₹ 108

S.P. of 1 article = ₹ $\dfrac{108}{12}$ = ₹ 9

(∵ S.P. is greater than C.P., means article is sold at a profit.)

Profit = S.P. - C.P.

= ₹ 9 - ₹ 7.5 = ₹ 1.5

$\text{Profit \%} = \dfrac{\text{Profit}}{\text{C.P.}} \times 100\%\\[1em] = \dfrac{1.5}{7.5} \times 100\%\\[1em] = \dfrac{150}{7.5}\%\\[1em] = \dfrac{1500}{75}\%\\[1em] = 20\%$

Hence, the profit percent = $20\%$.

(ii) Profit on 1 article = ₹ 1.5

Lets suppose $x$ articles are sold to make the profit of ₹ 75.

Profit on $x$ articles = ₹ 75

No. of articles x Profit on 1 article = Total Profit

$⇒ x \times 1.5 = 75\\[1em] ⇒ x = \dfrac{75}{1.5}\\[1em] ⇒ x = \dfrac{750}{15}\\[1em] ⇒ x = 50$

Hence, 50 articles need to be sold to make a profit of ₹ 75.