If, on a marked price, the difference between selling prices with a discount of 65% and with two successive discounts of 30% and 40% is Rs 105, then the marked price (in Rs) is : 

Options
a) 1650
b) 1050
c) 1500
d) 1320

Solution

As per question
D1 = 30%
D2 = 40%
Successive Discount = $ D_1 + D_2 = (\frac{D_1 \times D_2}{100})$
Successive Discount = $ 30 + 40 = (\frac{30 \times 40}{100})$
Successive Discount = 70 – 12
Successive Discount = 58%
Let the marked price be x
Selling price with a 65% discount:
SP1 = $ \frac{x – 65x}{100}$
SP1 = $ \frac{100x – 65x}{100}$
SP1 = $ \frac{35x}{100}$
Selling price with a 58% discount:
SP2 = $ \frac{x – 58x}{100}$
SP2 = $ \frac{100x – 58x}{100}$
SP2 = $ \frac{42x}{100}$

As per question
Difference is 105
$ \frac{42x}{100} – \frac{35x}{100}$ = 105
$ \frac{7x}{100}$ = 105
7x = 105 x 100
x = $ \frac{105 \times 100}{7}$
x = 1500

Answer: 1500