Question

Find a single discount to equal three consecutive discounts of 10%, 12% and 5%.

Answer 1

Let marked price be x
Now apply two successive discounts of 10%
%Discount = 10%
Discount price= Marked price(1-%Discount)
= x(1-(10/100))
= x(90/100)
= 0.9x
This is price 1
To this again 12% discount is availed.

%Discount= 12%
Discount price= price1(1-%Discount)
= 0.9x(1-(12/100))
= 0.9x(0.12)
= 0.108x
This is price2
To this again 5% discount is availed.

%Discount= 5%
Discount price= price2(1-%Discount)
= 0.108x(1-(5/100))
= 0.108x(0.05)
= 0.0054x
This is price3 or final price.

Now, find equivalent discount to successive discounts of 10%,12%,5%
Let equivalent discount be d

0.0054x = x - d% of x
=> d% of x = x-0.0054x
=>(d/100)×x= 0.9946x
=> d/100= 0.9946
=> d= 0.9946×100
•°• d= 99.46

•°• Effective %discount availed on successive discounts of 10%,12%,5% is 99.46%.

:)
Hope it helps