A vendor sold 25 laptops at a profit of 12% and 15 laptops at a profit of 20%. If he had sold all the 40 laptops at a profit of 18%, his profit would have increased by Rs. 30,000. What is the cost price of each laptop, if the cost price of all the 40 laptops is the same?

Correct option is C

Given:

Profit percentage of 25 laptops = 12%
Profit percentage of 15 laptops = 20%
Profit percentage of all the 40 laptops = 18%
Increase in profit = Rs. 30,000

Formula Used:

Profit % = $$(\frac{Profit }{Cost \ Price}) × 100$$​​

Solution:

Let the cost price of 1 laptop = Rs. x
The cost price of 25 laptops = Rs. 25x
The cost price of 15 laptops = Rs. 15x
The cost price of 40 laptops = Rs. 40x

Now, profit can be calculated as:

For 25 laptops:
​$$12 = (\frac{Profit }{25x}) × 100\\\ \\Profit = \frac{(12 × 25x)} {100}\\\ \\Profit = 3x$$​​

For 15 laptops:
​$$20 = (\frac{Profit }{15x}) × 100 \\\ \\Profit =\frac{ (20 × 15x)}{ 100} \\\ \\Profit = 3x$$​​

For 40 laptops:
​$$18 = (\frac{Profit }{40x}) × 100\\\ \\Profit = \frac{(18 × 40x) }{100}\\\ \\Profit = 7.2x$$​​

According to the question:
Profit of 40 laptops + Rs. 30,000 = Profit of 25 laptops + Profit of 15 laptops
7.2x + 30,000 = 3x + 3x
7.2x + 30,000 = 6x
1.2x = 30,000
x = 30,000 / 1.2
x = 25,000

Hence, the cost price of each laptop is Rs. 25,000.