A vendor mixed two varieties of rice costing ₹60 per kg and ₹45 per kg in the ratio 3 : 7. If he sells the mixed variety at ₹65 per kg, then what is his gain percentage? [Give your answer correct to two decimal places.]

A vendor mixed two varieties of rice costing ₹60 per kg and ₹45 per kg in the ratio 3 : 7.

Let's assume the quantities of two varieties mixed in 3y and 7y kg.

Cost price of mixture (each kg) = $$\frac{60\times\ 3y+45\times\ 7y}{3y+7y}$$

= $$\frac{180y+315y}{10y}$$

= $$\frac{495y}{10y}$$

= ₹49.5

If he sells the mixed variety at ₹65 per kg, then his gain percentage = $$\frac{(65-49.5)}{49.5}\times\ 100$$

= $$\frac{15.5}{49.5}\times\ 100$$

= 31.31%