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How many kilograms of sugar must be mixed?

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by Vemuri » Wed Apr 29, 2009 9:20 am
How many kilograms of sugar costing Tk. 9 per kg must be mixed with 27 kg of sugar costing Tk. 7 per kg so that there may be a gain of 10% by selling the mixture at Tk. 9.24 per kg?
A. 54 kg
B. 63 kg
C. 36 kg
D. 42 kg

OA is B. Is there a faster way of solving these kind of problems?
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by scoobydooby » Wed Apr 29, 2009 9:46 am
SP: 9.24 represents a gain of 10%, so CP must be 9.4*100/110=8.4

this CP can be set up as a weighted average equation. let x be the qty of sugar costing Tk. 9 per kg

x*9+27*7/(x+27)=8.4
=9x-8.4x=27(8.4-7)
=0.6x=27*1.4
=>x=63

hence, B

sure there is a smarter solution somewhere.
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by maihuna » Wed Apr 29, 2009 10:02 am
How many kilograms of sugar costing Tk. 9 per kg must be mixed with 27 kg of sugar costing Tk. 7 per kg so that there may be a gain of 10% by selling the mixture at Tk. 9.24 per kg?

CP = 9.24/1.1 = 8.4

Apply the dearence formula:

Dear*(Dear-Mean) = Cheap*(Mean-cheap)
x*(9-8.4) = 27*(8.4-7)
x = 27*1.4/0.6 = 27*7/3 = 63

figure:
9 7
8.4
1.4 0.6

ratio: 1.4/0.6 = 7/3
(7/3)*27 = 63
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