If the selling price is tripled and cost price doubled, the profit would become 65%. So, what is the present profit (in %)?

Given:

When the selling price is tripled and the cost price is doubled, the profit becomes 65%.

Let the original cost price be Rs. C and the original selling price be Rs. S.

Formula used:

New Selling Price (SP) = 3S

New Cost Price (CP) = 2C

Profit formula: Profit% = \(\frac{SP - CP}{CP} × 100\)

Given: Profit = 65%

So, \(\frac{3S - 2C}{2C} × 100 = 65\)

Calculation:

⇒ \(\frac{3S - 2C}{2C} = 0.65\)

⇒ 3S - 2C = 1.3C

⇒ 3S = 1.3C + 2C

⇒ 3S = 3.3C

⇒ S = 1.1C

So, the present selling price is 1.1 times the cost price, meaning the present profit is:

Profit% = \(\frac{S - C}{C} × 100\)

⇒ Profit% = \(\frac{1.1C - C}{C} × 100 = 0.1 × 100 = 10\%\)

∴ The present profit is 10%.

Shortcut Trick Let the present CP = 100

If CP is doubled then it is = 2 × 100 = 200

Profit = 65%

So, SP when CP is doubled = 200 × (165/100) = 330

330 is the tripled SP

So, original SP = 330/3 = 110

Present Profit = [(110 - 100)/100] × 100 = 10%

∴ The present profit is 10%.