Question

A shopkeeper buys coffee worth Rs 230 and tea worth Rs 150 . If he sells the coffee at 20 percent profit, at what profit percent must he sell the tea in order to earn 25 percent overall on selling the tea and coffee?

Answer 1

Hint: Firstly, we have to find the selling price (SP) of the coffee and the total selling price using the formula $SP=\left( \dfrac{100+\text{Gain}\%}{100} \right)CP$ . The total CP (Cost Price) can be found by adding the CP of tea and coffee. By subtracting the SP of coffee from the total SP, the SP of tea can be found. Then, we have to find the profit percentage of tea by substituting the CP and SP of tea in the formula $\text{Profit}\%=\dfrac{SP-CP}{CP}\times 100$ .

Complete step by step answer:
We are given the cost price (CP) of the coffee $=\text{Rs }230$ .
We are also given the profit percentage of coffee $=20\%$ .
Therefore, we can find the selling price (SP) of the coffee using the formula
$SP=\left( \dfrac{100+\text{Gain}\%}{100} \right)CP...\left( i \right)$
Let us substitute the values in the above formula.
\[\begin{align}
  & \Rightarrow S{{P}_{\text{coffee}}}=\left( \dfrac{100+20}{100} \right)230 \\
 & \Rightarrow S{{P}_{\text{coffee}}}=\left( \dfrac{120}{100} \right)\times 230 \\
 & \Rightarrow S{{P}_{\text{coffee}}}=\text{Rs }276 \\
\end{align}\]
We are also given that the CP of tea $=\text{Rs }150$ and the profit percentage of tea and coffee $=25\%$ .
Therefore, we can find the total CP by adding the CP of tea and coffee.
$\begin{align}
  & \Rightarrow \text{ Total CP}=\text{Rs 230}+\text{Rs 150} \\
 & \Rightarrow \text{ Total CP}=\text{Rs 380} \\
\end{align}$
Therefore, we can find the total SP using the formula (i).
$\begin{align}
  & \Rightarrow S{{P}_{\text{total}}}=\left( \dfrac{100+25}{100} \right)\times 380 \\
 & \Rightarrow S{{P}_{\text{total}}}=\left( \dfrac{125}{100} \right)\times 380 \\
 & \Rightarrow S{{P}_{\text{total}}}=\text{Rs }475 \\
\end{align}$
Thus, we can find the SP of tea by subtracting the SP of coffee from the total SP.
$\begin{align}
  & \Rightarrow S{{P}_{\text{tea}}}=S{{P}_{\text{total}}}-S{{P}_{\text{coffee}}} \\
 & \Rightarrow S{{P}_{\text{tea}}}=475-276 \\
 & \Rightarrow S{{P}_{\text{tea}}}=\text{Rs }199 \\
\end{align}$
Now, let us find the profit on tea by subtracting the CP from SP.
$\begin{align}
  & \Rightarrow \text{Profi}{{\text{t}}_{\text{tea}}}=SP-CP \\
 & \Rightarrow \text{Profi}{{\text{t}}_{\text{tea}}}=199-150 \\
 & \Rightarrow \text{Profi}{{\text{t}}_{\text{tea}}}=\text{Rs }49 \\
\end{align}$
Therefore, we can find the percentage profit of tea using the formula
$\begin{align}
  & \text{Profit}\%=\dfrac{SP-CP}{CP}\times 100 \\
 & \Rightarrow \text{Profit}\%=\dfrac{\text{Profit}}{CP}\times 100 \\
\end{align}$
Let us substitute the values in the above formula.
$\begin{align}
  & \Rightarrow \text{Profi}{{\text{t}}_{\text{tea}}}\%=\dfrac{49}{150}\times 100 \\
 & \Rightarrow \text{Profi}{{\text{t}}_{\text{tea}}}\%=\dfrac{98}{3} \\
 & \Rightarrow \text{Profi}{{\text{t}}_{\text{tea}}}\%=32.67\% \\
\end{align}$
Hence, the percentage of profit in selling tea is 32.67%.

Note: Students must learn the formulas of profit and loss to solve these types of questions. They have a chance of making a mistake by writing the formula for profit percentage as $\text{Profit}\%=\dfrac{CP-SP}{CP}\times 100$ which will lead to negative results. They must note that when a profit is incurred, the SP will be greater than CP and when a loss is incurred, the CP will be greater than the SP. The formula for percentage loss is given by $\text{Loss}\%=\dfrac{CP-SP}{CP}\times 100$ .