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(C) The selling price of the mixture is $Rs. 96/kg$ with a profit of $20\%$.$	ext{Cost Price (CP)} = \frac{	ext{Selling Price}}{1 + 	ext{Profit}\%}

Vedclass · Accepted Answer

$1: 4: 2$

Vedclass · Answer

(C) The selling price of the mixture is $Rs. 96/kg$ with a profit of $20\%$.$	ext{Cost Price (CP)} = \frac{	ext{Selling Price}}{1 + 	ext{Profit}\%} = \frac{96}{1.20} = Rs. 80/kg$.Let the three varieties be $A$ $(Rs. 60/kg)$,$B$ $(Rs. 75/kg)$,and $C$ $(Rs. 100/kg)$.We use the alligation method to find the ratio of quantities $Q_A, Q_B, Q_C$ to achieve a mean price of $Rs. 80/kg$.Step $1$: Compare $A$ and $C$ with the mean price $80$.$\frac{Q_A}{Q_C} = \frac{100 - 80}{80 - 60} = \frac{20}{20} = \frac{1}{1}$.Step $2$: Compare $B$ and $C$ with the mean price $80$.$\frac{Q_B}{Q_C} = \frac{100 - 80}{80 - 75} = \frac{20}{5} = \frac{4}{1}$.Step $3$: Equate the parts of $Q_C$ in both ratios. Since $Q_C$ is $1$ part in both,we combine them:$Q_A : Q_B : Q_C = 1 : 4 : (1 + 1) = 1 : 4 : 2$.

In what ratio must a person mix three kinds of tea costing $Rs. 60$ per $kg$,$Rs. 75$ per $kg$,and $Rs. 100$ per $kg$ so that the resultant mixture when sold at $Rs. 96$ per $kg$ yields a profit of $20\%$?

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