Question : A blended tea in a barrel contains Assam, Darjeeling, and Nilgiri Hills in a ratio of 2 : 3 : 1. Another barrel contains Darjeeling, Nilgiri Hills and Kangra Valley in a ratio 5 : 4 : 3. If equal weights of both blended teas are mixed together to make a new brand, then the weight of Kangra Valley tea per kilogram in the new brand is:
Option 1: 500 gm
Option 2: 100 gm
Option 3: 250 gm
Option 4: 125 gm
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Correct Answer: 125 gm
Solution :
Let's denote the weights of Assam, Darjeeling, and Nilgiri Hills teas in the first blend as $2x$, $3x$, and $x$ respectively. Similarly, let the weights of Darjeeling, Nilgiri Hills, and Kangra Valley teas in the second blend be $5y$, $4y$, and $3y$ respectively.
According to the question,
$2x+3x+x=5y+4y+3y$
⇒ $6x = 12 y$
⇒ $x=2y$
The weight of Kangra Valley tea in the second blend is $3y$, and the total weight of the blend is $12y + 6x = 24y$
So, the weight of Kangra Valley tea per kilogram
$=\frac{3y}{24y}\times 1000 =\frac{1}{8}\times 1000=125$ gm
Hence, the correct answer is 125 gm.
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