Question 18

# An owner of a grocery shop purchases two varieties of grain. The price of first variety is twice theÂ price of the second one. He mixes both the varieties and sells the mixture at the price of Rs. 28 per kg,Â making a profit of 25%. If the ratio of first variety of grain and the second variety of grain in theÂ mixture is 2:3, find the price of first variety of grain.

Solution

Let the mixture so created to be sold was exactly one kg.
Hence, amount of first variety procured to contribute to this mixture = (2/5)*1000 = 400gm or 0.4 kg
Hence, amount of second variety procured to contribute to this mixture = (3/5)*1000 = 600gm or 0.6 kg

Let the cost price of second variety = Rs. a/kg and hence, cost price of first variety = Rs. 2a / kg
Hence, cost price of the entire mixture = 0.6a + 0.4*2a = 1.4a rupees / kg

Also, the mixture is sold at Rs. 28 per kg and it means a profit of 25% ==> CP per kg = Rs. (28/1.25) per kg

Equating both, we get a = 16, hence, price of the first variety = 32 rupees per kg