Question

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.

Answer 1

Let number of articles bought = 60
Note: L.C.M of 15 and 12 = 60
$\therefore$ C.P. of the articles = Rs. $\frac{112.50}{15}\times 60$
=Rs. $\frac{112.50\times 60}{15}=112.50\times 4=Rs.450.00$
and S.P. of the articles = Rs. $\frac{108}{12}\times 60$
=Rs. 108 $\times$ 5 = Rs. 540
(i) Gain =S.P. - C.P. =Rs.540-Rs. 450
= Rs. 90
Gain% =$\frac{Gain}{C.P.}\times 100$
= $\frac{90}{450}\times 100=\frac{100}{5}$ =20%
(ii) To make a profit of Rs. 90, the number of articles needed to be sold = 60
To make a profit of Re. 1 the number of articles needed to be sold = $\frac{60}{90}$
To make a profit of Rs. 75, the number of articles needed to be sold
= $\frac{60}{90}\times 75=\frac{4500}{90}=50$