Question

The difference between the selling price on a discount of 32% and two successive discounts of 20% each on a certain bill is 25. Find the actual amount of the bill.

• A. 576
• B. 625
• C. 200
• D. 425

Answer 1

Answer:

B. 625

The actual amount of the bill is Rs. 625.

• Calculate the single discount:

  • The first discount rate is directly given as 32%.

• Calculate the equivalent single discount for the successive discounts:

  • When two successive discounts of 20% each are offered, we use the successive discount formula:
    $\text{Total Discount \%} = d_1 + d_2 - \frac{d_1 \times d_2}{100}$

  • Substitute $d_1 = 20$ and $d_2 = 20$:
    $\text{Total Discount \%} = 20 + 20 - \frac{20 \times 20}{100}$
    $\text{Total Discount \%} = 40 - 4 = \mathbf{36\%}$

• Find the percentage difference:

  • Since the bill amount is the same, the difference in selling prices is exactly equal to the difference between these two discount percentages:
    $36\% - 32\% = \mathbf{4\%}$

• Calculate the total bill amount:

  • We are given that this 4% difference equals Rs. 25.

  • If $4\%\text{ of Bill Amount} = \text{Rs. 25}$

  • Then $1\%\text{ of Bill Amount} = \frac{25}{4}$

  • Total Bill Amount ($100\%$) $= \frac{25}{4} \times 100 = 25 \times 25 = \mathbf{\text{Rs. } 625}$