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 mixture is worth Rs. 153 per kg, the price of the third variety per kg will be:
A. Rs. 169.50
B. Rs. 170
C. Rs. 175.50
D. Rs. 180
Answer: Option C
Solution(By Examveda Team)
Since first and second varieties are mixed in equal proportions.So, their average price
$$\eqalign{ & = {\text{Rs}}{\text{.}}\,\,\left( {\frac{{126 + 135}}{2}} \right) \cr & = {\text{Rs}}{\text{.}}\,\,130.50 \cr} $$
So, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x.
By the rule of alligation, we have:
$$\eqalign{ & \therefore \frac{{x - 153}}{{22.50}} = 1 \cr & \Rightarrow x - 153 = 22.50 \cr & \Rightarrow x = 175.50 \cr} $$
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Related Questions on Alligation
A. $$\frac{{1}}{{2}}$$ kg
B. $$\frac{{1}}{{8}}$$ kg
C. $$\frac{{3}}{{14}}$$ kg
D. $$\frac{{7}}{{9}}$$ kg
A. 81 litres
B. 71 litres
C. 56 litres
D. 50 litres
Fractions of different types of tea in the mixture are ¼, ¼ and ½ respectively. (Given, they are in ratio 1: 1: 2)
Say P is the price of third variety per kg.
⇒ 126 × (1/4) + 135 × (1/4) + P × (1/2) = 153
⇒ P/2 = 153 – 126/4 – 135/4
⇒ P/2 = 351/4
⇒ P = 351/2 = Rs.175.50 per kg