Tea Worth ₹126 per Kg and ₹135 per Kg Are Mixed with a Third Variety in the Ratio 1 : 1 : 2. If the Mixture is Worth ₹153 per Kg, the Price of the Third Variety per Kg Will Be - Mathematics

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MCQ

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

Options

  • ₹169.50

  • ₹170

  • ₹175.50

  • ₹180

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Solution

₹175.50
Explanation:

Since, first and second varieties are mixed in equal proportions.

So, their average price = ₹`((126+135)/2)=`₹130.50

So, the mixture is formed by mixing two varieties, one at ₹130.50 per kg and the other at say, ₹ x per kg in the ratio 2 : 2, i.e. 1 : 1. We have to find x.
By the rule of alligation, we have

\[\begin{array}{cc}
₹130.50\phantom{...........}₹x\\
\setminus \phantom{............}/ \\
\ce{\underset{₹153}{Mean Profit}}\\
/\phantom{............} \setminus \\
(x-153) \phantom{.........}22.50
\end{array}\]

∴ `("x"-153)/22.50=1/1`

⇒ x - 153 = 22.50 ⇒  x = ₹175.50

Concept: Ratio and Proportion (Entrance Exam)
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