Which of the following schemes provide the highest discount?

Correct option is B

Formula Used:

Total Discount = 100 - $$(1 - \frac{d_1}{100})(1 - \frac{d_2}{100}) \times 100$$​​

Solution:

A. Two successive discounts of 10% and 3%

Total Discount = $$100 - (1 - \frac{10}{100})(1 - \frac{3}{100}) \times 100$$​​

​$$= 100 - (0.9 \times 0.97) \times 100$$​​

​$$= 100 - 0.873 \times 100 = 100 - 87.3 = 12.7\%$$​​

B. Two successive discounts of 10% each

Total Discount = $$100 - (1 - \frac{10}{100})(1 - \frac{10}{100}) \times 100$$​​

​$$= 100 - (0.9 \times 0.9) \times 100$$​​

​$$= 100 - 0.81 \times 100 = 100 - 81 = 19\%$$​​

C. Two successive discounts of 7% and 10%

Total Discount  = $$100 - (1 - \frac{7}{100})(1 - \frac{10}{100}) \times 100$$​​

​$$= 100 - (0.93 \times 0.9) \times 100$$​​

​$$= 100 - 0.837 \times 100 = 100 - 83.7 = 16.3\%$$​​

D. Two successive discounts of 5% and 10%

Total Discount = $$100 - (1 - \frac{5}{100})(1 - \frac{10}{100}) \times 100$$​​

​$$= 100 - (0.95 \times 0.9) \times 100$$​​

​$$= 100 - 0.855 \times 100 = 100 - 85.5 = 14.5\%$$​​

The highest discount is provided by B: Two successive discounts of 10% each, with a total discount of 19%.