How many kilogram of sugar costing Tk. 9 per kg must be mixed with 27 kg of sugar costing Tk. 7 per kg so that there may be a gain of 10% by selling the mixture at Tk. 9.24 per kg?

Question: How many kilogram of sugar costing Tk. 9 per kg must be mixed with 27 kg of sugar costing Tk. 7 per kg so that there may be a gain of 10% by selling the mixture at Tk. 9.24 per kg?Solution:Let,Quantity of sugar costing Tk. 9 per kg = xS.P. of 1 kg of mixture = Tk. 9.24, Gain 10%.C.P. of 1 kg of mixture = Tk. (100/110) × 9.24 = Tk. 8.40By the rule of allilation, we have:⇒ 27 : x = (9 - 8.40) : (8.40 - 7) = 0.60 : 1.40 = 6 : 14 = 3 : 7⇒ 27/x = 3/7⇒ x/27 = 7/3⇒ x = (7 × 27)/3∴ x = 63