Applied to a bill for ₹1000, what is the difference between a discount of 40% and two successive discounts of 36% and 4%?

The correct answer is ₹14.40.

We need to find the difference between two discount schemes applied to a bill of ₹1000:

Scheme A: A single discount of 40%
Scheme B: Two successive discounts of 36% and 4%

Step 1: Calculate the final price under Scheme A (Single 40% discount)

Discount amount = 40% of ₹1000

=\frac{40}{100}\times 1000=\mathrm{₹400}

Price after Scheme A = ₹1000 - ₹400 = ₹600

Step 2: Calculate the final price under Scheme B (Successive discounts of 36% then 4%)

First discount of 36%:

\text{Price after 1st discount}=1000\times \frac{100-36}{100}=1000\times \frac{64}{100}=\mathrm{₹640}

Second discount of 4% on the reduced price:

\text{Price after 2nd discount}=640\times \frac{100-4}{100}=640\times \frac{96}{100}=\mathrm{₹614.40}

Step 3: Find the Difference

Scheme B gives a smaller total discount than Scheme A (since two successive discounts are always less effective than a single equivalent combined discount). So the customer pays more under Scheme B.

\text{Difference}=\text{Price under Scheme B}-\text{Price under Scheme A}

=614.40-600=\mathrm{₹14.40}

Why is there a difference?
When two successive discounts of r₁% and r₂% are applied, the effective single discount is:

\text{Effective discount}=r_1+r_2-\frac{r_1\times r_2}{100}

=36+4-\frac{36\times 4}{100}=40-1.44=\mathrm{38.56\%}

So Scheme B effectively gives only a 38.56% discount, compared to the 40% in Scheme A. The difference in discount percentage = 40% - 38.56% = 1.44% of ₹1000 = ₹14.40 ✓

Therefore, the difference between the two discount schemes is ₹14.40.