A grocer used a defective balance and gave $$4.8\text{ kg}$$ of almond at Rs. 4800 per kg to a customer. The customer was in doubt about the weight. So, he asked the grocer to put the almond bag in the other pan. Surprisingly it weighed only $$2.7\text{ kg}$$. The grocer apologised and charged the amount for only $$3750\text{ g}$$ (that is average of $$4.8\text{ kg}$$ and $$2.7\text{ kg}$$) of almond. In doing so, the grocer still earned the profit. Find the percentage profit of the grocer.

Let the arms of the balance be $$L_1$$ and $$L_2$$ and the true weight of the bag be $$w$$. The two weighings give $$w L_1 = 4.8 L_2$$ and $$2.7 L_1 = w L_2$$; dividing, $$\frac{w}{2.7} = \frac{4.8}{w}$$, so $$w^2 = 4.8 \times 2.7 = 12.96$$ and $$w = 3.6\text{ kg}$$. The almonds given are worth $$3.6 \times 4800 = 17280$$ rupees, while the customer paid for $$3.75\text{ kg}$$, that is $$3.75 \times 4800 = 18000$$ rupees. Profit percentage $$= \frac{18000 - 17280}{17280} \times 100 = \frac{100}{24} = 4\frac{1}{6}\% \approx 4.17\%$$.