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Alligation or Mixture

Q1: 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?

A 36 kg

B 42 kg

C 54 kg

D 63 kg

ANS:D - 63 kg

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 1st kind Cost of 1 kg sugar of 2nd kind
Rs. 9 Mean Price
Rs. 8.40 		Rs. 7
1.40 0.60
Ratio of quantities of 1st and 2nd kind = 14 : 6 = 7 : 3. Let x kg of sugar of 1st be mixed with 27 kg of 2nd kind. Then, 7 : 3 = x : 27
x = 7 x 27 = 63 kg.
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