Question

Joshep marks up an article by x% gives a discount of \(\frac{x}{{20}}\) % and gets a profit of \(\frac{{3x}}{4}\% \). Had he marked up by \(\frac{{7x}}{8}\) % and gives a discount of \(\frac{x}{{12}}\)%, then, what would be his profit percentage?
1. 200%
2. 100%
3. 250%
4. 320%
5. None of these

Answer 1

Correct Answer - Option 1 : 200%

Concept used:

Profit % = (Profit/CP) × 100

Discount % = (Discount/MP) × 100

Calculation:

The cost price of an article is ₹ 100.

For case I:

Cost Price	Marked Price	Selling Price	Profit
100	(100 + x)	\(\left( {100 + x} \right) \times \left( {\frac{{100 - \frac{x}{{20}}}}{{100}}} \right)\)	\(\frac{{3x}}{4}\)% of 100 = 3x/4

 

  From above table –

⇒ \(\left( {100 + x} \right) \times \left( {\frac{{100 - \frac{x}{{20}}}}{{100}}} \right) = \left( {100 + \frac{{3x}}{4}} \right)\)

⇒ (100 + x) × (2000 – x) = 2000 × (100 + 3x/4)

⇒ 200,000 + 2000x – 100x – x² = 200,000 + 1500x

⇒ 1900x – x² = 1500x

⇒ 1900x – 1500x = x²

⇒ 400x = x²

⇒ x = 400

For case II:

Cost Price = 100

The marked price = (100 + 7x/8% of 100)

⇒ 100 + {(7 × 400)/(8 × 100)} × 100

⇒ 100 + 350 = 450

The selling price = 450 – x/12 % of 450

⇒ 450 – 400/12 % of 450

⇒ 300

∴ Profit = SP – CP = 300 – 100 = 200

Profit % = (Profit/CP) × 100

⇒ Profit % = (200/100) × 100

⇒ Profit % = 200%

∴ the profit % = 200%