A dealer buys dry fruit at the rate of Rs. 100, Rs. 80 and Rs. 60 per kg. He bought them in the ratio 12 : 15 : 20 by weight. He in total gets 20% profit by selling the first two and at last he finds he has no gain no loss in selling the whole quantity which he had. What was the percentage loss he suffered for the third quantity ?

Solution(By Examveda Team)

Suppose he bought 12 kg, 15 kg and 20 kg of the three varieties respectively.
Then,
Total C.P. = Rs. (12 × 100 + 15 × 80 + 20 × 60)
= Rs. (1200 + 1200 + 1200)
= Rs. 3600
Let the loss on the third quantity be x%
Than,
=120% of 2400 +(100 - x)% of 1200 = 3600
$$\eqalign{ & \Rightarrow \left( {\frac{6}{5} \times 24} \right) + \left( {\frac{{100 - x}}{{100}} \times 12} \right) = 36 \cr & \Rightarrow \frac{{100 - x}}{{100}} \times 12 = 36 - \frac{{144}}{5} = \frac{{36}}{5} \cr & \Rightarrow \frac{{100 - x}}{{100}} = \frac{{36}}{5} \times \frac{1}{{12}} = \frac{3}{5} \cr & \Rightarrow 500 - 5x = 300 \cr & \Rightarrow 5x = 200 \cr & \Rightarrow x = 40\% \cr} $$