Two qualities of rice at Rs.63 per kg and Rs.67.50 per kg are mixed with another quality of rice in the ratio 2:2:3. The final mixture sold at Rs.76.50 per kg then the rate of third quality rice per kg was:
Given that, first and 2nd varieties are mixed in equal proportion.
Their average price = Rs.(63 + 67.50) / 2 = Rs.65.25
The new mixture is formed by mixing two varieties, one at Rs.65.25 per kg and the other at Rs.X per kg in the ratio 4:3. (note that, 2:2:3 becomes 4:3).
Given that, mean price of new mixture = Rs.76.50
We have to find X.
Applying the rule of alligation,Therefore, (Cheaper quantity) : (Dearer quantity) = (d - m) : (m - c) =
X - 76.50 / 11.25 = 4/3
3X – 229.50 = 45
X = 91.50
Hence, the required price of 3rd quality rice = Rs.91.50.
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