Question : One quality of rice at INR 45 per kg is mixed with another quality at a certain rate in the ratio of 3 : 2. If the mixture so formed is worth INR 50 per kg, what is the rate per kg of the second quality of rice?
Option 1: INR 57
Option 2: INR 57.5
Option 3: INR 58
Option 4: INR 58.5
Correct Answer: INR 57.5
Solution :
One quality of rice is sold at = INR 45 per kg
The mixture so formed is worth = INR 50 per kg
Let the rate of second quality be INR $x$ per kg
Ratio = 3 : 2
Let the total quantities of rice = 3 + 2 = 5 kg
$\frac{\text{Total Price of One Quality Rice}+\text{Total Price of Second Quality Rice}}{\text{Total kg Rice}} = {\text{Rate of Mixture}}$
⇒ $\frac{45\times{3}+2x}{5} = 50$
⇒ $135 + 2x = 250$
⇒ $x = 57.5$
$\therefore$ The rate of the second quality of rice is INR 57.5.
Hence, the correct answer is INR 57.5.
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