Question : Rice worth INR 35 per kilogram and INR 38 per kilogram are mixed with a third variety in the ratio 2 : 1 : 2. If the mixture is worth INR 42 per kilogram, the price of the third variety per kilogram is:
Option 1: INR 52
Option 2: INR 53
Option 3: INR 54
Option 4: INR 51
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Correct Answer: INR 51
Solution :
Given ratio = 2 : 1 : 2
Let the price of the third variety be INR $x$.
Let us take 2 kg, 1 kg, and 2 kg of rice worth INR 35 per kg, INR 38 per kg, and INR $x$ per kg, respectively.
Total worth of (2 kg + 1 kg + 2kg) = 5 kg of mixture is 35 $\times$ 2 + 38$ \times$ 1 + $x \times$ 2
= 70 + 38 + 2$x$
= 108 + 2$x$ .....(1)
According to the question,
1 kg of mixture = INR 42
Worth of 5 kg of mixture = (42 × 5) = INR 210.......(2)
$\therefore$ from equations (1) and (2),
108 + 2$x$ = 210
⇒ 2$x$ = 102
$\therefore$ $x$ = INR 51
Hence, the correct answer is INR 51.
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