Question

Find a single discount equivalent to the two successive discounts of 15% and 20%..
Please answer to this question...​

Answer 1

Well let consider an Amount of 100.rs

first discount 20% = 80 rs

second discount 15% of 80 rs = 68 rs

therefore it's equivalent to 32%

Answer 2

Answer:

32%

Step-by-step explanation:

 Let the price be 'a'.

At first:

  Price = a - 15% of a

= a(1 - 15%) = a(1 - 0.15)

= a(0.85)

 Again:

Price = a(0.85)(1 - 20%)

= a(0.85)(1 - 0.20) = a(0.68)

   % = a - a(0.68)/a  * 100%

       = a(1 - 0.68)/a  * 100%

       = a(0.32)/a  * 100%

       = 32%

In general, if 'a' is price. And it first increases/decreases by x% and then y%. So,

 First:  a(1 + x%)

 At 2nd:  a(1 + x%)(1 + y%)

% = [a(1 + x%)(1 + y%) - a]/a * 100%

   = [(1 + x%)(1 + y%)-1] * 100%

   = (1 + y% + x% + x%y% - 1]100%

   = (x% + y% + x%y%]*100%

   = (x/100 + y/100 + xy/10000]*100%

   = [ x + y + xy/100 ] %

It can be used as general formula. In this case. x = -15 , y = -20

⇒ [-15 -20 + (-15*-20)/100]%

⇒ [-35 + 300/100]&

⇒ - 32%

          total disc. = 32%