A dealer buys dry fruit at the rate of Rs. 100, Rs. 80 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)

Let the weights of the three varieties be 12x, 15x and 20x kg respectively
Then,

Total C.P. = Rs. (100 × 12x + 80 × 15x + 60 × 20x)
= Rs. (3600x)
S.P. of the first two verities
$$\eqalign{ & = {\text{Rs}}.\left( {\frac{{120}}{{100}} \times 2400x} \right) \cr & = {\text{Rs}}.\left( {2880x} \right) \cr & {\text{S}}{\text{.P}}{\text{. of the third variety}} \cr & = {\text{Rs}}.\left( {3600x - 2880x} \right) \cr & = {\text{Rs}}{\text{. }}720x \cr & {\text{Loss on third variety}} \cr & = {\text{Rs}}{\text{.}}\left( {1200x - 720x} \right) \cr & = {\text{Rs}}{\text{. }}480 \cr & {\text{loss }}\% \cr & = \left( {\frac{{480x}}{{1200x}} \times 100} \right)\% \cr & = 40\% \cr} $$