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 ) ]%