If a shop gives 30% discount and then provides another 20% discount, then the total discount will be

The correct answer is (C) 44%.

• Formula and Given Data: Let the marked price of the article be 100. Successive discounts of 30% and 20% are applied. The effective net discount percentage for two successive discounts $a\%$ and $b\%$ is given by the formula: $\text{Net Discount}=(a+b-\frac{a\times b}{100})\mathrm{\%}$$\text{Net Discount}$ = \left(a + b - $\frac{a \times b}{100}$\right)\%.
• Step-by-step Calculation: First discount ($a$) = 30%, Second discount ($b$) = 20%. Substituting the values into the formula: $\text{Net Discount}=(30+20-\frac{30\times 20}{100})\mathrm{\%}=(50-\frac{600}{100})\mathrm{\%}=(50-6)\mathrm{\%}=44\mathrm{\%}$$\text{Net Discount}$ = \left(30 + 20 - $\frac{30 \times 20}{100}$\right)\% = \left(50 - $\frac{600}{100}$\right)\% = (50 - 6)\% = 44\%. Alternatively, price after first discount = $100 - 30\%$$\text{ of }$ 100 = 70. Price after second discount = $70 - 20\%$$\text{ of }$ 70 = 70 - 14 = 56. Total discount = $100 - 56 = 44$.
• Option Verification: Option (A) 50% is incorrect as it simply adds the discounts without accounting for the compounding effect. Option (B) 42% and Option (D) 56% are mathematical errors resulting from incorrect operations. Thus, Option (C) 44% is verified as correct.