A shopkeeper sold a product at 30% loss. Had his selling price been ₹150 more, he would have made a profit of 10%. What was the cost price ?
[amp_mcq option1=”₹375″ option2=”₹400″ option3=”₹425″ option4=”₹450″ correct=”option1″]
This question was previously asked in
UPSC CAPF – 2024
Initially, the shopkeeper sold the product at a 30% loss.
Selling Price 1 (SP1) = CP – 30% of CP = CP – 0.30 * CP = 0.70 * CP.
If the selling price had been ₹150 more, he would have made a profit of 10%.
Selling Price 2 (SP2) = SP1 + ₹150.
Also, SP2 represents a 10% profit on the cost price.
SP2 = CP + 10% of CP = CP + 0.10 * CP = 1.10 * CP.
So, we have the equation:
0.70 * CP + 150 = 1.10 * CP.
Subtract 0.70 * CP from both sides:
150 = 1.10 * CP – 0.70 * CP
150 = 0.40 * CP.
To find CP, divide 150 by 0.40:
CP = $\frac{150}{0.40} = \frac{150}{\frac{4}{10}} = \frac{150 \times 10}{4} = \frac{1500}{4}$.
CP = 375.
SP2 – SP1 = ₹150.
SP2 = CP + 10% profit = 1.10 CP.
SP1 = CP – 30% loss = 0.70 CP.
SP2 – SP1 = 1.10 CP – 0.70 CP = 0.40 CP.
So, 0.40 CP = 150.
CP = 150 / 0.40 = 375.