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Mixture and Alligation #9

9. How many kilograms 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. 56 kgB. 58 kg
C. 63 kgD. 60 kg

Answer: Option C

Explanation:

Selling Price(SP) of 1 kg mixture= Rs. 9.24

Profit = 10%

Cost Price(CP) of 1 kg mixture $=\dfrac{100}{(100+\text{Profit}\%)}× \text{SP}$
$=\dfrac{100}{(100+10)}× 9.24\\= \dfrac{100}{110}× 9.24=\dfrac{92.4}{11}=\text{ Rs.} 8.4$

By rule of alligation,

CP of 1 kg sugar of 1st kindCP of 1 kg sugar of 2nd kind
Rs. 9Rs. 7
Mean Price
Rs.8.4
8.4 - 7 = 1.49 - 8.4 = 0.6

i.e., to get a cost price of 8.4, the sugars of kind1 and kind2 should be mixed in the ratio 1.4 : 0.6 = 14 : 6 = 7 : 3

Suppose $x$ kg of kind1 sugar is mixed with 27 kg of kind2 sugar.
then $x$ : 27 = 7 : 3
$\Rightarrow 3x=27×7\\\Rightarrow x=9×7=63$

Comments(2)

profilertt
2013-11-16 13:22:11 
ans=51.98
like 0 dislike 0 reply
profileNarendra
2013-11-16 19:18:50 
Pl explain how you reached this answer
like 0 dislike 0

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