Question

Reshma sells an article to Rekha at \(37.5\%\) profit, Rekha sells it to Madhu at \(9\dfrac{1}{11}\%\) profit. Again Madhu sells it to Mitu at \(25\%\) loss. If Mitu pays Rs.~\(342\) for the article, then what is the cost price of the article to Reshma?

• A. Rs.~304
• B. Rs.~266.50
• C. Rs.~380
• D. Rs.~384.75

Hint:

For successive profit/loss problems, replace each percentage with a multiplicative factor and multiply along the chain. To reverse, divide by the overall factor.

Answer 1

The Correct Option is A

Step 1: Convert the percentage changes to multipliers.
\(37.5%=\frac{3}{8}\Rightarrow\) profit factor \(=1+\frac{3}{8}=\frac{11}{8}\).
\(9\dfrac{1}{11}%=\frac{1}{11}\Rightarrow\) profit factor \(=1+\frac{1}{11}=\frac{12}{11}\).
\(25%\) loss \(\Rightarrow\) loss factor \(=1-\frac{1}{4}=\frac{3}{4}\).
Step 2: Let the cost price to Reshma be \(x\). Track the chain of transactions.
After Reshma’s sale (to Rekha): selling price \(=x\cdot\frac{11}{8}\) \(\Rightarrow\) this is Rekha’s cost.
After Rekha’s sale (to Madhu): selling price \(=x\cdot\frac{11}{8}\cdot\frac{12}{11}=x\cdot\frac{12}{8}=x\cdot\frac{3}{2}\).
After Madhu’s sale (to Mitu) with \(25%\) loss: final price \[ \text{Mitu pays }=x\cdot\frac{3}{2}\cdot\frac{3}{4}=x\cdot\frac{9}{8}. \] Step 3: Use the given final price to find \(x\).
\[ x\cdot\frac{9}{8}=342\ \Rightarrow\ x=342\cdot\frac{8}{9}=38\cdot 8=304. \] \[ \boxed{\text{Rs.~304}} \]