The difference between a discount of 27% and two successive discounts of 20% and 10% on a certain bill was Rs. 56. Find the amount of the bill.

A single discount of 27%.

Two successive discounts of 20% and 10%.

The difference in the discount amounts between these two discount methods is Rs.56.

The effective discount for two successive discounts is given by:

​$$\text{Effective Discount} = a + b - \frac{a \cdot b}{100}$$​​

​$$\text{Effective Discount} = 20 + 10 - \frac{20 \times 10}{100} = 30 - 2 = 28\%$$​​

Now, Let the bill amount be x.

Single Discount Amount = 0.27 × x

Successive Discount Amount = 0.28 × x

Given that the difference in discount amounts is Rs. 56:

0.28x − 0.27x = 56

0.01x = 56

x = $$\frac{56}{0.01}$$​ = 5600

Thus, The amount of the bill is Rs. 5600.