A clock was sold for Rs 144. If the profit percentage was numerically equal to the cost price, what was the cost price of the clock?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Rs 80
Profit per cent is taken on the cost price, so selling price \(=\) cost price \(+\) profit % of the cost price. Taking the cost price as Rs \(x\) makes the profit \(x\%\) too.
Cost price \(=\) Rs \(x\), profit \(=x\%\) of \(x\) \(\displaystyle =\frac{x^{2}}{100}\)
\(\displaystyle x+\frac{x^{2}}{100}=144\)
\(x^{2}+100x-14400=0\)
\((x-80)(x+180)=0\)
The cost price cannot be negative, so \(x=80\)
Check: 80% of Rs 80 \(=\) Rs 64, and \(80+64=144\)
The cost price of the clock was Rs 80.