find the single discount percentage equivalent ti three successive discounts of 10%,5% and 2%
Answers
Step-by-step explanation:
Given:-
Three successive discounts of 10%,5% and 2%
To find:-
Find the single discount percentage equivalent three successive discounts of 10%,5% and 2%?
Solution:-
General method:-
Let the Marked Price of an article be
Rs. X
First discount percentage on it = 10%
Discount =10% of Rs. X
=>(10/100)×X
=>(1/10)× X
=>X/10
First Discount = Rs. X/10
Price of the article after first discount =
=>X-(X/10)
=>(10X-X)/10
=>9X/10
The price of the articel after 10% discount
= Rs. 9X/10
Now, The second discount percentage on it = 5%
Discount = 5% of (9X/10)
=>(5/100)×(9X/10)
=>(1/20)×(9X/10)
Second Discount=9X/200
The price of the article after getting second discount 5%
=>(9X/10) - (9X/200)
=>(180X-9X)/200
=>171X/200
The price of the article after 5% discount =
Rs. 171X/200
The third discount percentage of the article=2%
Discount = 2% of 171X/200
=>(2/100)×(171X/200)
=>(1/50)×(171X/200)
Third Discount =171X/10000
The price of the article after getting the third discount = (171X/200)-(171X/10000)
=>[(171X×50)-(171X)]/10000
=>(8550X-171X)/10000
=>8379X/10000
Price of the article after getting third discount 2% on it = Rs. (8379X/10000)
Total discount = First discount +Second discount+Third discount
=>Total discount= (X/10)+(9X/200)+(171X/10000)
=>(1000X+450X+171X)/10000
Total discount on it =1621X/10000
Discount Percentage =
(Discount/Marked Price)×100
D% =[ (1621X/10000)/X]×100
=>D% = (1621X/10000X)×100
=>D% = (1621×100)/10000
=>D% = 162100/10000
=>D%=1621/100
=>D% = 16.21%
The total discount on it = 16.21%
Method -2:-
Successive discounts = 10% , 5% and 2%
If the first discount is x% and 2nd discount is y% then ,
Total discount =[ ( x + y - (xy / 100 ) ]%
We have x = 10% and y= 5%
=>[(10+5-(5×10/100)]
= 15-(50/100)
=>15-(1/2)
=>(30-1)/2
=>29/2%
And again x= 29/2% and y=2%
=>[{(29/2)+2}-{(29/2)×2}/100]
=>(29+4)/2-(29/100)
=>(33/2)-(29/100)
=>33/2-0.29
=>16.5-0.29
=>16.21%
Answer:-
The Single discount for the given problem is 16.21%
Used formula:-
If the first discount is x% and 2nd discount is y% then ,
Total discount =[ ( x + y - (xy / 100 ) ]%