Source: Previous Question Papers

Due to increase in the prices of fruits by 20%, the sale was decreased by 10%. Find the percent increase or decrease in the income of the fruitseller.

Options

Option A

10% increase

Option B is correct

8% increase

Option C

8% decrease

Option D

10% decrease

Explanation

Let the original price of fruits be PP and the original quantity sold be QQ.The original income (IoriginalI_{original}) of the fruitseller is Ioriginal=P×QI_{original} = P \times Q.The prices of fruits increased by 20%, so the new price (PnewP_{new}) is:Pnew=P+0.20P=1.20PP_{new} = P + 0.20P = 1.20PThe sale (quantity) decreased by 10%, so the new quantity sold (QnewQ_{new}) is:Qnew=Q0.10Q=0.90QQ_{new} = Q - 0.10Q = 0.90QThe new income (InewI_{new}) of the fruitseller is:Inew=Pnew×Qnew=(1.20P)×(0.90Q)=(1.20×0.90)×(P×Q)=1.08PQI_{new} = P_{new} \times Q_{new} = (1.20P) \times (0.90Q) = (1.20 \times 0.90) \times (P \times Q) = 1.08PQTo find the percent change in income, we use the formula: Percent Change=InewIoriginalIoriginal×100%\text{Percent Change} = \frac{I_{new} - I_{original}}{I_{original}} \times 100\% Percent Change=1.08PQPQPQ×100%\text{Percent Change} = \frac{1.08PQ - PQ}{PQ} \times 100\% Percent Change=0.08PQPQ×100%\text{Percent Change} = \frac{0.08PQ}{PQ} \times 100\% Percent Change=0.08×100%\text{Percent Change} = 0.08 \times 100\% Percent Change=8%\text{Percent Change} = 8\%Since the result is positive, it is an 8% increase in income.