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(C) The selling price of the mixture is $Rs. 30/kg$ and the profit is $20\%$. The cost price of the mixture is $\frac{30}{1.2} = Rs. 25/kg$.Let the qu

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$5$

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(C) The selling price of the mixture is $Rs. 30/kg$ and the profit is $20\%$. The cost price of the mixture is $\frac{30}{1.2} = Rs. 25/kg$.Let the quantities of the three varieties be $Q_A, Q_B,$ and $Q_C$ with costs $20, 24,$ and $30$ respectively.Using the alligation rule for the mixture:For $Q_A$ and $Q_C$: $\frac{Q_A}{Q_C} = \frac{30 - 25}{25 - 20} = \frac{5}{5} = \frac{1}{1}$.For $Q_B$ and $Q_C$: $\frac{Q_B}{Q_C} = \frac{30 - 25}{25 - 24} = \frac{5}{1}$.To combine these,we equate the $Q_C$ parts. In both ratios,$Q_C$ is $1$ unit. Thus,the ratio $Q_A : Q_B : Q_C = 1 : 5 : 1$.Wait,the total $Q_C$ is the sum of parts from both alligations: $Q_C = 1 + 1 = 2$ units.So,the ratio is $Q_A : Q_B : Q_C = 1 : 5 : 2$.Given $Q_C = 2$ $kg$,the quantity of the second variety $Q_B = 5$ $kg$.

$A$ merchant mixes three varieties of rice costing $Rs. 20$ per $kg$,$Rs. 24$ per $kg$,and $Rs. 30$ per $kg$ and sells the mixture at a profit of $20\%$ at $Rs. 30$ per $kg$. How many $kgs$ of the second variety will be in the mixture if $2$ $kgs$ of the third variety is there in the mixture?

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