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

36 kg
42 kg
54 kg
63 kg

Correct Answer: 63 kg

Explanation:

S.P. of 1 kg of mixture = Rs. 9.24, Gain 10%.

∴ C.P. of 1 kg of mixture = Rs.	❨	100	x 9.24	❩	= Rs. 8.40
		110

By the rule of allilation, we have:

C.P. of 1 kg sugar of 1^st kind Cost of 1 kg sugar of 2^nd kind
Rs. 9	Mean Price Rs. 8.40	Rs. 7
1.40		0.60

∴ Ratio of quantities of 1^st and 2^nd kind = 14 : 6 = 7 : 3.

Let x kg of sugar of 1^st be mixed with 27 kg of 2^nd kind.

Then, 7 : 3 = x : 27

⟹ x =	❨	7 x 27	❩	= 63 kg.
		3

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