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Tea Mixture problem

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by lkm » Mon Aug 02, 2010 6:14 pm
Question:

Tea worth Rs 126 per kg and Rs 135 per kg are mixed with a third variety in the ratio 1:1:2. If the new mixture is worth Rs 153 per kg, the price of the third variety per kg will be:

A) 164.25
B) 169.50
C) 170.0
D) 175.50
E) 180

Please also tell how to deal with such problems.
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by indiantiger » Mon Aug 02, 2010 6:32 pm
so you are given the ratio of mixture that is prepared from three varieties of tea

each ratio gives the amount in kg of that tea variety so we can say the ratio is as follows

x : x : 2x

Lets say the price of third variety is P
now total price / kg can be calculated as



126*x + 135*x + 2x*P / (x+x+2x)----(1)

x+x+2x represents the total weight

we know the mixtures price/kg = 153 --- (2)

from (1) and (2) we can get
126*x + 135*x + 2x*P / (x+x+2x) = 153
126+135 +2P = 4 * 153
261+2P = 612
P = 612-261 / 2
P = 175.5 (D) answer
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by Rahul@gurome » Mon Aug 02, 2010 6:33 pm
Let the price of third variety be x.

So if the three varieties are mixed in the ratio 1:1:2, then the price of mixture per kg is
(126*1 + 135*1 + x*2)/(1+1+2) = (261+2x)/4.
It is given that (261+2x)/4 = 153
Or 2x = 351
Or x = 351/2 = 175.5

The correct answer is (D).
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