Question

Find the single discount equivalent to two successive discounts of 20% and 10%
(a) 28%
(b) 29%
(c) 30%
(d) 26%

Answer 1

Hint: First, we will assume any number on which we will find two successive discounts given. So, we will take the number to be 100. Then by using the formula \[\left( x-discount\%\cdot x \right)\] where x is the number we assumed, we will find first for 20% and then taking x to be the answer we got , on 10%. At last, we will use the same formula where we have to find a discount%. Thus, on solving we will get the answer.

Complete step-by-step answer:
Here, we will first assume any number of which will find the two successive discounts. So, we will assume that number to be 100.
Now, 20% discount on 100 will be given as \[\left( x-discount\%\cdot x \right)\] where x is 100 in this case. So, using this we will get as
\[\left( 100-\dfrac{20}{100}\cdot 100 \right)=100-20=80\]
Now, again we will find a 10% discount on 80. So, we will get as
\[\left( 80-\dfrac{10}{100}\cdot 80 \right)=80-8=72\]
Thus, successive discounts i.e. 20% and 10% on 100 is 72.
So, now we will see how much percent of 100 is equal to 72. So, here the formula used will be \[\left( x-discount\%\cdot x \right)\] where we have to find a discount%. So, we will get as
\[100-\dfrac{y}{100}100=72\]
On solving, we will get as
\[100-72=y\]
\[28=y\]
Thus, the answer is 28%. Option (a) is the correct answer.

Note: Another method to find successive discounts is by using the formula \[\left( x+y-\dfrac{xy}{100} \right)\%\] where x, y are discount values. So, by putting values and solving them we get an equation as \[\left( 20+10-\dfrac{20\cdot 10}{100} \right)\%\] . On further solving, we get as \[\left( 30-2 \right)\%=28\%\] . Thus, we will get the same answer.