Question

If on a marked price, the difference of selling prices with a discount of 30% and two successive discounts of 20% and 10% is 72, then the marked price (in rupees) ?

• A. 3,600
• B. 3,000
• C. 2,500
• D. 2,400

Hint:

Always carefully calculate the effective discount for successive discounts ($d_1, d_2$): $d_{eff} = d_1 + d_2 - \frac{d_1 d_2}{100}$. Then use this to find the selling price. A single discount of $X\%$ means the selling price is $(100-X)\%$ of the marked price.

Answer 1

The Correct Option is A

Step 1: A single 30% discount leaves 70% of the marked price (MP) as the selling price, so \( SP_1 = 0.70 \times MP \).

Step 2: Two successive discounts of 20% and 10% are equivalent to one combined discount of \( 20+10-\frac{20\times10}{100}=28\% \), so \( SP_2 = 0.72 \times MP \).

Step 3: The difference is \( SP_2 - SP_1 = 0.02 \times MP = 72 \), so \( MP = \frac{72}{0.02} \).
\[ \boxed{MP = Rs.\ 3{,}600} \]