Question

A shopkeeper marks 30% above cost and allows a 15% discount. He also uses a faulty balance: sells “1 kg” but delivers only 800 g. Find his actual profit percentage.

• A. 38.125%
• B. 24.425%
• C. 32.124%
• D. None of these

Hint:

For false weights, compute SP on the billed quantity but CP on the actual quantity delivered.

Answer 1

The Correct Option is A

Assume cost price (CP) per kg $=₹ 100$.
Marked price $=100\times1.30=₹ 130$. After 15% discount, billed SP per “kg” $=130\times0.85=₹ 110.5$.
But he supplies only $0.8$ kg, whose cost to him $=0.8\times100=₹ 80$.
Profit $=₹(110.5-80)=₹ 30.5$.
Profit % $=\dfrac{30.5}{80}\times100=38.125%$. \(\Rightarrow\) Includes hidden gain from short-weight ($1/0.8=1.25$, i.e., $25%$ extra). \boxed{\text{Actual Profit }=38.125%}