The marked price of an article is Rs. 450. It is sold for Rs. 348.48, after giving two successive discounts each of x% on the marked price. If a single discount of 2x% is given on the same marked price, then what will be its selling price?

Shortcut Trick

Discount = 450 - 348.48 = 101.52

Discount % = (101.52/450) × 100 = 22.56

We have both discounts the same i.e. x, therefore

⇒ x + x - (x²/100) = 22.56 

⇒ 2x - (x²/100) = 22.56

Here, successive discount % is same 

So, we can say 22.56 will be near to double of that discount

Taking x = 12 by hit and trial

⇒ 24 - (144/100) = 22.56 (Satisfies the condition)

Hence, we can say the value of x = 12

Now for 2nd situation the Discount = 2x = 24%

⇒ SP = 450 × (100 - 24)/100 = 450 × 76/100

⇒ SP = 342

Hence, The selling price after a single discount is Rs. 342

Alternate Method

Given: 

Marked price MP = 450

Selling Price SP for successive discount = 348.48

Formula used:  

Discount = MP - SP

Successive Discount (D) = x + y - (xy/100)

Where x and y are values of discount

SP = MP × (100 - Discount%)/100

Factors = \( {-b \pm √{b^2-4ac} \over 2a}\)

Calculation:

Discount = 450 - 348.48 = 101.52

D% = (101.52/450) × 100 = 22.56

We have both discounts the same i.e. x, therefore

⇒ x + x - (x²/100) = 22.56

⇒ 200x - x² = 2256

⇒ x² - 200x + 2256 = 0     -----(1)

Here, a = 1, b = -200, and c = 2256

Using the formula \( {-b \pm √{b^2-4ac} \over 2a}\)

⇒ x = [- (-200) + √(200² - 4 × 1 × 2256)]/2

⇒ x = (200 + √30976)/2

⇒ x= (200 + 176)/2 = 188

And x =  [- (-200) - √(2002 - 4 × 1 × 2256)]/2

⇒ x = (200 - √30976)/2

⇒ x= (200 - 176)/2 = 12

Solving the eq(1) for the values of x we get

⇒ x = 12 and 188

The required value of x = 12

Now for 2nd situation the Discount = 2x = 24%

⇒ SP = MP × (100 - Discount%)/100

⇒ SP = 450 × (100 - 24)/100 = 450 × 76/100

⇒ SP = 342

Hence, The selling price after a single discount is Rs. 342