# 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} 0 votes 23 views in Aptitude closed 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

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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%