Question

Prove the formula of successive discount or how to derive it

Answer 1

Successive Discount : The formula for total discount in case of successive-discounts : 
If the first discount is x% and 2nd discount is y% then ,
Total discount = ( x + y - xy / 100 ) %Example : 

1) The successive-discount of 10% and 20% are given on the purchase of a bag . If the price of the bag is $ 2250, find the selling price.

Solution: 
As the successive discount is 10% and 20% 

Total discount = ( x + y - xy / 100 ) % 

x = 10% and y = 20% 

Total discount = [ 10 + 20 – ( 10 x 20) / 100] % 

= ( 30 – 200 /100 ) % 

Total discount = 28% 

Discount = 28% of 2250 

Discount = ( 28 / 100 ) x 2250 

Discount = $630 

S.P = M.P – Discount 

= 2250 – 630

Selling price = $ 1620 

2) If the discounts on the printed price of an item are 20% and 12½ and 5 % respectively, what is the total percentage of actual discount?

Solution : 
First we will find out the total discount between the first two discounts.

Total discount = ( x + y - xy / 100 ) % 

Here, x = 20% and y = 12 ½ 

Consider the discount of 20% and 12½ = r %

Total discount of 20% and 12½ = [ 20 + 12½ - (20 x 12 ½)/100 ] % 

= [ 20 + 12.5 - ( 20 x 12.5)/100 ]%

= ( 32.5 - 2.5)%

= 30%

Now the final discount between 5% and 30%

Total discount = ( r + z - rz / 100 ) % 

Here, r = 30% and z = 5%

Total discount of 30% and 5% = [ 30 + 5 - (30 x 5)/100]%

= ( 35 - 150/100)%

= ( 35 - 1.5)%

= 33.5%

So the total single discount is 33.5%

Note : If there are three discounts as x% , y% and z% then find the total discount of x % and y% first and using it find the total discount with z%

Answer 2

Successive Discount : The formula for total discount in case of successive-discounts : 
If the first discount is x% and 2nd discount is y% then ,
Total discount = ( x + y - xy / 100 ) %Example : 

1) The successive-discount of 10% and 20% are given on the purchase of a bag . If the price of the bag is $ 2250, find the selling price.