Successive Discount Formula

What is Successive Discount?

It is basically offering a discount on a product multiple times i.e. one discount after another.

For Example – If a product costs ₹1000 and you get a 20% discount followed by a 10% discount, the final price is not ₹1000 – 30%, but rather:

First discount: ₹1000 – 20% = ₹800

Second discount: ₹800 – 10% = ₹720
So, the final price = ₹720 (not ₹700)

Note –

• It is quiet obvious that for 100, after giving x% discount the price will be 100 – x. So, (100 – 10) = 90
• For 90 we do same thing again we calculate 20% 90, which easily can be 2x(10% of 90) = 2x(9) =18
• So 20 % now is 18, thus after discount price will be 90 – 18 = Rs72.
• Thus for 1000. 72(1000/100) = Rs720 Answer

Now that was easy but now let’s suppose they had said, discounts were 17% and 24% then the process becomes a little tricky but we guarantee once you practice this trick you can solve any problem within 20 seconds.

• For 17 it is easy, since we can calculate 100 – 17 = 83.
• Now for next we use approximation.
  • First calculate 10% of 83 = 8.3, so 20% = 2(8.3) = 16.6
  • Then 1% of 83 = .83, so 4% = (.8)4 = 3.2.
  • Above we used approximation
  • So total 24% is = (16.6 + 3.2) 19.8 approx 20.
  • So Answer would be option closest to 83 – 20 = 63

Now the above problem may look confusing but if you practice enough. The whole above problem will take about 45 seconds.

We discourage using this formula below since, you can learn a formula for every problem. But for two successive discounts this is the formula, you can’t clear exams like eLitmus if you don’t build mental strength to solve the above.

Case 1: If there are two discounts(Two Successive Discount Formula):

The formula for total discount in case of successive-discounts: 
If the first discount is x% and 2nd discount is y% then Successive Discount Formula –

Total discount = ( x + y – xy /100)%

Example: The marked price of a shirt is Rs.1000. A shopkeeper offers 10% discount on this shirt and then again offers 20% discount on the new price. How much will you have to pay, finally?

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 ) % = 28% 

Discount = 28% of 1000 = ( 28 / 100 ) x 1000 = Rs 280

Selling price (SP)= Marked price (MP) – Discount = 1000-280 = Rs720

Case 2: If there are three discounts(Three Successive Discount Formula):

 It means discount on the discount on the discount. (Analogous to Compound Interest rate which signifies interest on interest)

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%

Example: The marked price of a shirt is Rs.1000. A shopkeeper offers 10% discount on this shirt and then again offers 20% discount on the new price, and then and then again offers 30% discount on the new price . How much will you have to pay, finally?

Solution: 

As the successive discount is 10% and 20% and then again 30%.Here we will move step by step and first calculate it for only two discounts, and then whatever the result comes, again calculating it fotr the result we got and the remaining discount.

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

• x = 10%, y = 20% and z = 30%
• Total discount = [10 + 20 – (10 x 20) / 100] % = (30 – 200 /100) % = 28% (let us say d)

Now, d= 28 % & z = 30 %

Total discount = (d + z – dz / 100) % 

• Final discount = [28 + 30 – (28 x 30) / 100] % = (58 – 840 /100) % = 49.6% 
• Which means Discount = 49.6% of 1000 = (49.6 / 100) x 1000 Rs 496
• Selling price = M.P – Discount = 1000- 496 = 504

Tips and Tricks to Solve Successive Discount based Questions

The most important question is which discount is better among Successive discount and One Time Discount. So here by means of an example, we will explain the simple tricks to solve these Successive Discount based question quickly

Example: The marked price of a shirt is Rs.1000. A shopkeeper offers

Case 1: 10% discount on this shirt and then again offers 20% discount on the new price.

Case 2: 29 % discount

Which is the better deal?

Solution:

• Case 1: We have already solved case 1 & the net discount came out to be 28 % only, means Selling price = Rs 720
• Case 2: In case 2 we are getting Flat 29% discount which means, this deal is better for you as Selling price = Rs 710

But to arrive to this point we have to do a hell lot of calculation.What you can do is use shortcut technique

• Case 1: Successive discount 10% and then 20%, Final price you’ve to pay = 0.90 x 0.80 x original price = 0.72 x original price
• Case 2: Discount offered=29%, Final price you’ve to pay = 0.71 times original price, which is less than Case 1, means it is abetter deal.