Single discount rate equivalent to a series of discounts 20% and 25 is

Let the marked price be ₹ 100

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Solution(By Examveda Team)
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After 1st discount the price = 100`(1 - 10/100)`

= 90

After 2nd discount the price = 90`(1 - 20/100)`

= 72

After 3rd discount the price = 72`(1 - 15/100)`

= `72 xx 85/100`

= 61.2

∴ The selling price after 3 discounts is ₹ 61.2.

∴ Single equivalent discount

= marked price – selling price

= 100 – 61.2

= ₹ 38.8

∴ The single equivalent discount is ₹ 38.8 on ₹ 100.

i.e. The single equivalent discount is 38.8%.

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.

Examveda

A single discount equivalent to the successive discounts of 10%, 20% and 25% is = ?

A. 55%

B. 45%

C. 46%

D. 60%

Answer: Option C

Solution(By Examveda Team)

Let the price is = Rs. 100
After discount price
$$\eqalign{ & {\text{ = 100}} \times \frac{{90}}{{100}} \times \frac{{80}}{{100}} \times \frac{{75}}{{100}} \cr & {\text{ = Rs}}{\text{. 54}} \cr & {\text{Difference = 100}} - 54 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 46\% \cr} $$
So, 46% is a single discount of percent of this series.

Alternate :
Successive discount of 10% of 20%
$$\eqalign{ & = 10 + 20 - \frac{{10 \times 20}}{{100}} \cr & = 28\% \cr} $$
Then successive discount of 28% and 25%
$$\eqalign{ & = 28 + 25 - \frac{{28 \times 25}}{{100}} \cr & = 46\% \cr} $$