If on a marked price, the difference between selling prices with a discount of 45% and two successive discounts of 30% and 20% is ₹84, then the marked price is ____________.

Correct option is A

Given:

Difference in selling prices = ₹84

First scenario: Single discount = 45%

Second scenario: Successive discounts = 30% and 20%

Formula Used:

SP after discount = $$MP \times\left(1 - \frac{discount}{100}\right)$$​​

Solution:

SP(single discount) = $$MP \times (1 - \frac{45}{100}) = MP \times 0.55$$​​

SP (successive discounts) = $$MP \times (1 - \frac{30}{100}) \times (1 - \frac{20}{100}) = MP \times 0.7 \times 0.8 = MP \times 0.56$$​​

Now,

​$$MP \times 0.56 - MP \times 0.55 = 84$$​​

​$$MP \times (0.56 - 0.55) = 84$$​​

​$$MP \times 0.01 = 84$$​​

​$$MP = \frac{84}{0.01} = ₹8400$$​​

Alternate Solution:

Net effective discount = $$30 + 20 -\frac{20 \times 30}{100}$$​ = 44%

Now,

56% - 55% = 84

1% = 84

100% = ₹8400