Find a single discount equivalent to two successive discounts of 12% and 8%.

Let's assume the MRP of an article is 100y.

Price after first discount = 100y of (100-12)%

= 100y of 88%

= 88y

Price after second discount = 88y of (100-8)%

= 88y of 92%

= $$88y\times\frac{92}{100}$$

= 80.96y

single discount equivalent to two successive discounts = $$\frac{\left(100y-80.96y\right)}{100y}\times\ 100$$

= $$\frac{19.04y}{100y}\times\ 100$$

= 19.04%

Shortcut ::

single discount equivalent to two successive discounts = 12%+8%-$$\frac{12\times\ 8}{100}$$%

= 12%+8%-$$\frac{96}{100}$$%

= 12%+8%-0.96%

= 20%-0.96%

= 19.04%