Question : Wheat worth Rs. 80 per kg and Rs. 50 per kg is mixed with a third variety in the ratio $1:2:3$. If the mixture is worth Rs.75 per kg, then the price of the third variety per kg will be equal to:
Option 1: Rs. 95
Option 2: Rs. 85
Option 3: Rs. 80
Option 4: Rs. 90
Correct Answer: Rs. 90
Solution :
Let the price of the third variety be Rs. $x$ per kg.
The ratio of varieties of rice in the mixture is $1 : 2 : 3$.
Let the amount of the first, second, and third varieties of rice in the mixture be 1 kg, 2 kg, and 3 kg respectively.
⇒ Total quantity of the mixture = (1 + 2 + 3) kg = 6 kg
⇒ Total amount of the mixture = 1 × 80 + 2 × 50 + 3$x$ = 180 + 3$x$
Now, the price of the mixture per kg is Rs. 75.
⇒ $\frac{(180 + 3x)}{6} = 75$
⇒ 180 + 3$x$ = 450
⇒ 3$x$ = 270
$\therefore x$ = 90
Hence, the correct answer is Rs. 90.
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