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 – x^{2 }= 200,000 + 1500x
⇒ 1900x – x^{2} = 1500x
⇒ 1900x – 1500x = x^{2}
⇒ 400x = x^{2}
⇒ 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%