Question : 49 kg of blended tea contains Assam and Darjeeling teas in the ratio 5 : 2. The quantity of Darjeeling tea to be added to the mixture to make the ratio of Assam to Darjeeling tea 2 : 1 is:
Option 1: 4.5 kg
Option 2: 3.5 kg
Option 3: 5 kg
Option 4: 6 kg
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Correct Answer: 3.5 kg
Solution :
Given:
The ratio of Assam tea to Darjeeling tea in 49 kg of a blend = 5 : 2
According to the question statement,
Quantity of Assam tea = $\frac{5}{7}$ × 49 = 35
Quantity of Darjeeling tea = 49 – 35 = 14
Let the quantity of Darjeeling tea added be $x$ kg.
According to the question,
⇒ $\frac{35}{(14 + x)}=\frac{2}{1}$
⇒ 35 = 28 + 2x
⇒ 2x = 7
$\therefore$ x = 3.5 kg
Hence, the correct answer is 3.5 kg.
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