How many kilogram of sugar costing Rs. 9 per kg must be mixed with 27 kg of suga

Question

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?

Options:

A . 36 kg

B . 42 kg

C . 54 kg

D . 63 kg

Answer: Option D

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

So, C.P. of 1 kg of mixture = Rs. \(\left(\frac{100}{110}\times9.24\right)=Rs. 8.40\)

By the rule of allilation, we have:

C.P. of 1 kg sugar of 1^st kind = Rs.9

Cost of 1 kg sugar of 2^nd kind = Rs.7

Main Price = Rs. 8.40

So, 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= \(\left(\frac{7\times27}{3}\right)= 63 kg.\)

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