A wholesaler purchased 150 ceramic vases for a total cost of ₹600. During transit, 18 of the vases broke completely and could not be sold. At what price should each remaining undamaged vase be sold to secure an overall profit of 25% on the initial investment?

Correct Answer: ₹5.68

Step-by-step Explanation:

Step 1: Identify the total initial investment (Cost Price).
The wholesaler purchased 150 ceramic vases for a total cost of ₹600.

$\text{Total Cost Price (CP)}=\text{₹600}$

Step 2: Find the number of remaining undamaged vases.
Out of the 150 vases, 18 were broken during transit and could not be sold.

$\text{Undamaged Vases}=150-18=132$

Step 3: Calculate the total required revenue to achieve a 25% profit.
To secure an overall profit of 25% on the initial investment of ₹600, calculate the profit amount first:

$\text{Profit}=25\%\text{of ₹600}=\frac{25}{100}\times 600=\text{₹150}$

$\text{Total Revenue Required}=\text{Cost Price}+\text{Profit}=600+150=\text{₹750}$

Step 4: Calculate the selling price for each undamaged vase.
The wholesaler must earn a total of ₹750 by selling the 132 undamaged vases. Divide the total revenue by the number of undamaged vases:

$\text{Selling Price per Vase}=\frac{\text{Total Revenue Required}}{\text{Number of Undamaged Vases}}$

$\text{Selling Price per Vase}=\frac{750}{132}=5.681818...\approx \text{₹5.68}$

Thus, each remaining undamaged vase should be sold for ₹5.68 to secure an overall profit of 25%.