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Mixture and Alligation #2

2. Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety of tea in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, what is the price of the third variety per kg ?
A. Rs.175.50B. Rs.180
C. Rs.182.50D. Rs.170.5

Answer: Option A

Explanation:

Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed in the ratio 1 : 1
So their average price $=\dfrac{\left(126 + 135 \right)}{2} = 130.5$

Hence let's consider that the mixture is formed by mixing two varieties of tea, one at Rs. 130.50 per kg and the other at Rs. $x$ per kg in the ratio 2 : 2, i.e., 1 : 1. Now let's find out $x$.

By rule of alligation,

Cost of 1 kg of 1st kind of teaCost of 1 kg of 2nd kind of tea
130.50$x$
Mean Price
153
$(x-153)$22.50

$(x-153):22.5=1:1\\\Rightarrow x-153=22.50\\\Rightarrow x=153+22.5=175.5$

Comments(4)

profileAshish
2015-05-21 10:48:20 
Mixture is 4 kg so
126*1+135*1+2*x/4=153
261+2x=153*4
2x=351
x=175.50
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profilemango_man
2014-02-22 18:20:42 
Posted in yahoo by some user


1 : 1 :2
let x be the third mixture
126: 135 :2x = 153

:>(126 + 135 + 2x)/4 = 153
(261 + 2x ) =4*153
2x = 612 - 261
2x = 351
:. x = 175.50

:>the price of the third variety per kg: 175.50
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profiled
2014-04-22 09:41:07 
hw it came divided by 4?
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profileSandhya
2014-07-10 15:51:30 
the sum of the ratios 1+1+2=4...soo did divided by 4.

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