Question

A vendor bought shirts worth ₹10000 and sold half of them at a gain of 25%. Half of the remaining were sold at a profit of 10%. At what price should he sell remaining shirts to gain 15% on the entire transaction (in rupees)?

• A. 2500
• B. 2400
• C. 2600
• D. 2900

Hint:

In successive profit and loss problems, always work with the cost price of each portion separately and compare the accumulated revenue with the desired total revenue.

Answer 1

The Correct Option is A

Concept: For a desired overall profit, first calculate the total selling price required. Then subtract the revenue already obtained from previous sales to determine the selling price of the remaining goods.

Step 1: Calculate the total selling price required for a 15% profit.
Total Cost Price \[ = ₹10000 \] Desired profit \[ =15\% \] Hence required total selling price is \[ 10000+\frac{15}{100}\times10000 \] \[ =10000+1500 \] \[ =₹11500 \]

Step 2: Calculate the revenue from the first sale.
Half of the shirts have cost price \[ =\frac{10000}{2}=₹5000 \] These are sold at a gain of \(25\%\). Therefore selling price is \[ 5000+\frac{25}{100}\times5000 \] \[ =5000+1250 \] \[ =₹6250 \]

Step 3: Calculate the revenue from the second sale.
Remaining shirts have cost price \[ =₹5000 \] Half of these are sold. Cost price of this portion \[ =\frac{5000}{2}=₹2500 \] Sold at \(10\%\) profit. Hence selling price is \[ 2500+\frac{10}{100}\times2500 \] \[ =2500+250 \] \[ =₹2750 \]

Step 4: Find the selling price of the remaining shirts.
Revenue already obtained \[ =6250+2750 \] \[ =₹9000 \] Required total revenue \[ =₹11500 \] Therefore revenue still needed \[ =11500-9000 \] \[ =₹2500 \] Hence the remaining shirts should be sold for \[ \boxed{₹2500} \]