
Find the single discount equivalent to two successive discounts of 20% and 10%
(a) 28%
(b) 29%
(c) 30%
(d) 26%
Answer
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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 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 where x is 100 in this case. So, using this we will get as
Now, again we will find a 10% discount on 80. So, we will get as
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 where we have to find a discount%. So, we will get as
On solving, we will get as
Thus, the answer is 28%. Option (a) is the correct answer.
Note: Another method to find successive discounts is by using the formula where x, y are discount values. So, by putting values and solving them we get an equation as . On further solving, we get as . Thus, we will get the same 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
Now, again we will find a 10% discount on 80. So, we will get as
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
On solving, we will get as
Thus, the answer is 28%. Option (a) is the correct answer.
Note: Another method to find successive discounts is by using the formula
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