The marked price of an article is Rs. 875. It is sold for Rs. 598.50, after giving three successive discounts of 10%. x% and 20%. What is the selling price of the article, if it is sold at a single discount of 3x% ?

Correct option is A

Given:

Marked Price (MP) = Rs. 875

Selling Price (SP) after three successive discounts = Rs. 598.50

The successive discounts are 10%, x%, and 20%.

Formula Used:

SP = MP $$\times \left(1 - \frac{d_1}{100}\right) \times \left(1 - \frac{d_2}{100}\right) \times \left(1 - \frac{d_3}{100}\right)$$​​

Solution:

for the three successive discounts:

​$$598.50 = 875 \times 0.90 \times \left(1 - \frac{x}{100}\right) \times 0.80$$​​

​$$598.50 = 875 \times 0.72 \times \left(1 - \frac{x}{100}\right)$$​​

​$$598.50 = 630 \times \left(1 - \frac{x}{100}\right)$$​​

​$$\frac{598.50}{630} = 1 - \frac{x}{100}$$​​

​$$0.95 = 1 - \frac{x}{100}$$​​

​$$\frac{x}{100} = 0.05$$​​

x = 5

Now Selling price for a single discount of 3x = 15%:

SP = $$875 \times \left(1 - \frac{15}{100}\right)$$​​

= 875 × 0.85 = Rs. 743.75