QUESTION

# A grocer sells 5 chocolates for Rs. 1 at a profit of 4%. In order to get a profit of Rs 30, how many chocolates does he have to sell for Rs. 1?

Hint: To solve the question, we have to apply a profit percentage formula to calculate the cost price of 5 chocolates and use the obtained value to cost the price of one chocolate. Apply the same formula for the second case of profit using the calculated cost price of one chocolate to obtain the selling price of one chocolate. Thus, we can arrive at the answer by dividing the cost of RS. 1 to the calculated selling price of one chocolate.

Let the cost price of 5 chocolates be Rs. x
The given selling price of 5 chocolates = Rs. 1
The given profit percentage obtained by selling 5 chocolates for Rs. 1 = 4%
We know that the profit percentage is given by the formula, $P=\left( \dfrac{SP-CP}{CP} \right)\times 100$
Where P, CP, SP represent the profit percentage, cost price and selling price.
By substituting the values in the above mentioned formula, we get
\begin{align} & 4=\left( \dfrac{1-x}{x} \right)\times 100 \\ & \dfrac{4}{100}=\left( \dfrac{1-x}{x} \right) \\ & 0.04=\dfrac{1-x}{x} \\ & \Rightarrow 0.04x=1-x \\ & x+0.04x=1 \\ & 1.04x=1 \\ & x=\dfrac{1}{1.04}=0.96 \\ \end{align}
Thus, the cost price of 5 chocolates is equal to Rs. 0.96
We know the cost price of 1 chocolate is equal to the ratio of cost of n chocolates to n.
Thus, we get the cost price of 1 chocolate is equal to $\dfrac{0.96}{5}=Rs.0.192$
For profit percentage of 30, the selling price is given by
\begin{align} & 30=\left( \dfrac{SP-0.192}{x} \right)\times 100 \\ & \dfrac{30}{100}=\left( \dfrac{SP-0.192}{0.192} \right) \\ & 0.3=\dfrac{SP-0.192}{0.192} \\ & \Rightarrow 0.3\times 0.192=SP-0.192 \\ & 0.0576+0.192=SP \\ & SP=0.2496\approx 0.25 \\ \end{align}
Thus, we get the selling price is equal to Rs. 0.25
The number of chocolates can be sold for Rs.1 = Ratio of Rs.1 to the calculated selling price for 1 chocolate.
$\dfrac{1}{0.25}=\dfrac{100}{25}=4$
Thus, he has to sell 4 chocolates for Rs. 1 to obtain profit of Rs.30.

Note: The possibility of mistake can be, not profit percentage formula to calculate the cost price of 5 chocolates. The alternative method to solve the equation is to compare and solve, for the first case, 5 chocolates the SP is Rs. 1 and profit is 4% which implies SP is 104% times the CP and for the second case, n chocolates the SP is Rs. 1 and profit is 30% which implies SP is 130% times the CP. We can calculate the n value which represents the number of chocolates can be sold for Rs.1 to obtain profit of Rs.30.