A shopkeeper makes a net profit of 44% on selling an article at successive discounts of 10% and 20%. Find the net profit percentage, if the shopkeeper sells the same article at a discount of 15%.

Given:

A shopkeeper makes a net profit of 44% on selling an article at successive discounts of 10% and 20%. 

Concept used:

1. Selling Price = Marked Price × (1 - Discount%)

2. Selling Price = Cost Price × (1 + Gain%)

Calculation:

Final discount% = \(10 + 20 - \frac {10 × 20}{100}\) = 28%

Let the marked and cost price be  = \(10 + 20 - \frac {10 × 20}{100}\) = 28% respectively.

​According to the question,

MP(1 - 28%) = CP(1 + 44%)

⇒ 0.72 × MP = 1.44 × CP

⇒ MP = 2CP

If a 15% discount is allowed then the selling price

⇒ MP(1 - 15%)

⇒ 0.85MP

⇒ 0.85 × 2CP = 1.7CP

Now, profit% = \(\frac {1.7CP - CP}{CP} × 100\%\) = 70%

∴ The net profit is 70%.

Shortcut Trick

Final discount% = \(10 + 20 - \frac {10 × 20}{100}\) = 28%

So, MP : SP = 100 : 72 

Here, shopkeeper makes a net profit of 44%

So, CP : SP = 100 : 144

Now, CP : SP : MP = 100 : 144 : 200

Now, 15% discount given then SP = 200 × 85/100 = 170

So, profit% is 70/100 × 100 = 70%