Find the single discount equivalent to two successive discounts of 10% and 5%.

Let's assume the price before discounts is '100y'.

Price after discounts = 100y of (100-10)% of (100-5)%

= 100y of 90% of 95%

= $$100y\times\frac{90}{100}\times\frac{95}{100}$$

= 85.5y

Let's assume the single discount is 'z'%.

100y of (100-z)% = 85.5y

$$100y\times\frac{(100-z)}{100}=85.5y$$

$$(100-z)=85.5$$

z = 100-85.5

z = 14.5%

Short Cut ::

successive discount = $$10\%+5\%-\left(\frac{10\times\ 5}{100}\right)\%$$

= $$15\%-0.\ 5\%$$

= 14.5%