Question

The cost price of a pen increases by Rs. 10. The selling price increases by 25%. If the new profit increases from 20% to 25%, what is the original cost price per pen?​

Answer 1

Step-by-step explanation:

Let us assume,

• The original CP of pen be x.

As given,

• The gain% on original CP is 25%.

Finding the SP on original CP,

• ➠ SP = [(100 + gain%)/100] × CP
• ➠ SP = [(100 + 20)/10] × x
• ➠ SP = 120/100 × x
• ➠ SP = 6/5 x

We found,

• The SP on original CP is 6/5 x.

Finding the Increased CP,

• The increased CP of pen will be x + 10.

Finding the SP on original CP,

• ➠ SP' = [(100 + gain%)/100] × CP
• ➠ SP' = [(100 + 25)/10] × (x + 10)
• ➠ SP' = 125/100 × (x + 10)
• ➠ SP' = [5(x + 10)]/4
• ➠ SP' = (5x + 50)/4

We found,

• The SP on Increased CP is (5x + 50)/4

As we know that,

• Increase% = Difference/(Original value) × 100

So we can say that,

• ➠ 25 = [(5x + 50)/4 - 6x/5]/(6x/5) × 100
• ➠ 25/100 = [(5{5x + 50} - 4{6x}})/20] / (6x/5)
• ➠ 1/4 = (25x + 250 - 24x)/20 × 5/6x
• ➠ 1/4 × 6x/5 = (x + 250)/20
• ➠ 6x/20 × 20 = x + 250
• ➠ 6x - x = 250
• ➠ 5x = 250
• ➠ x = 250/5
• ➠ x = ₹50

Hence,

• The original CP is ₹50.

Finalized Answer:

• The original CP of pen is ₹50.