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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 kg B. 58 kg C. 63 kg D. 60 kg

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 kind CP of 1 kg sugar of 2nd kind Rs. 9 Rs. 7 Mean Price Rs.8.4 8.4 - 7 = 1.4 9 - 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
$\Rightarrow 3x=27×7\\\Rightarrow x=9×7=63$

rtt
2013-11-16 13:22:11
ans=51.98