Question

14. Find the single discount equivalent to two successive
discounts of 8% and 5%.​

Answer 1

Answer:

The single discount = 12.6%

Step-by-step explanation:

Discount of 8% applied on "x" would mean:

x - 8% of x             (Original value less 8% of the original value)

= x - 0.08x

= 0.92x

Applying a successive discount of 5% on 0.92x, we get

0.92x - 5% of 0.92x

= 0.9x - 0.05*(0.92x)

= (1 - 0.05)*(0.92x)

= (0.95)*(0.92x)

= 0.874x

Now:

The initial value of "x" has reduced to "0.874x" after the two discounts.

0.874x = (1 - 0.126)*x

            = x - 0.126x

             = x - 12.6% of x

This means that 0.874x is same as applying a 12.6% discount on x.

=> Discount of 8% and 5% applied successively implies a single discount of 12.6%