Question : In what ratio does a grocer mix tea at INR 26 per kg and INR 32 per kg so that by selling the mixture at INR 30 per kg he may gain 10%?
Option 1: 7 : 26
Option 2: 16 : 7
Option 3: 26 : 7
Option 4: 7 : 16
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Correct Answer: 26 : 7
Solution :
Given: A grocer mixes tea at INR 26 per kg and INR 32 per kg so that by selling the mixture at INR 30 per kg he may gain 10%.
Selling price = INR 30 per kg and gain = 10%.
So, the cost price of the mixture = $\frac{30×100}{110}$ = INR $\frac{300}{11}$ per kg.
Now, let the ratio be $x:y$.
According to the question,
$26x+32y=\frac{300}{11}(x+y)$
$⇒\frac{300x}{11}-26x=32y-\frac{300y}{11}$
$⇒14x = 52y$
$\therefore x:y = 26:7$
Hence, the correct answer is 26 : 7.
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