Question

A shopkeeper sold 24 pens at a profit of 25% and 20 same quality pens at a profit 15%. The profit would have been Rs. 5.6 less if all the pens were sold at a profit of 20%. What is the cost price each pen?

1. Rs. 56
2. Rs. 45
3. Rs. 36
4. Rs. 28
5. Rs. 60

Answer 1

Correct Answer - Option 4 : Rs. 28

Given:

24 pens sold at 25% profit

20 pens sold at 15% profit

Difference in profit if all were sold at 20% profit is Rs. 5.6

Formula:

Sp = (100 + x)% of Cp

Where,

Sp = Sell price

Cp = Cost price

x = Profit percent

Calculation:

Let the cost price of each pen be x

Total pens = 24 + 20 = 44

Total cost price = 44x

Cost price of 24 pens = 24x

Sell price of 24 pens = 125% of 24x = 30x

Cost price of other 20 pens = 20x

Sell price of the other 20 pens = 115% of 20x = 23x

Total sell price = 30x + 23x = 53x

Sell price if all were sold at a profit of 20% = 120% of 44x = 52.8x

Difference in profits = 53x – 52.8x = 0.2x

0.2x = 5.6

⇒ x = 5.6/0.2

⇒ x = 56/2

⇒ x = 28

∴ Cost price of each pen is Rs. 28