Important Formulas: Profit and Loss | Quantitative for GMAT PDF Download

Formulas for Profit and Loss

• Cost Price – It is basically the price at which a commodity or object is bought at. e.g. Shopkeeper buying Sugar from Farmer to sell in his grocery store. In its short form it is denoted as C.P.
• Selling Price – The price at which the commodity is sold at. e.g. Shopkeeper selling sugar to his customer. In its short form is denoted as S.P.
• Gain or Profit – If Cost Price is lesser than Selling Price, gain is made.
• Loss – If Cost price is greater than the Selling price, Loss is incurred.

1.  C.P in case of gain:

2.  C.P in case of Loss:

3. S.P in case of Gain:

4. S.P in case of Loss:

Other Important Formulas for Profit and Loss

Important Formulas for Profit and Loss

• Profit = Selling Price – Cost Price
• Loss = Cost Price – Selling Price
• Profit % = (Profit / Cost Price) × 100%
• Loss% = (Loss / Cost Price) × 100%
• Selling Price = [(100 + Profit%)/100] × Cost Price
• Cost Price = [100/(100 + Profit%)] × Selling Price
• Selling Price = [(100 – Loss%)/100] × Cost Price
• Cost Price = [100/(100 – Loss%)] × Selling Price
• Discount = Marked Price – Selling Price

Successive Discount Formula

• 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.

Case 1: If there are two discounts
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?
Sol: 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:

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?
Sol: 
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 Succesive 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 baesed questuion 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?
Sol:

• 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.

Increase and Decrease Percentage Problem

• It is quiet obvious that for 100, after giving x% discount the price will be 100 – x. So, (100 – 40) = 60
• For 60 we do same thing again we calculate 50% increase, which easily can be 5x(10% of 60) = 5x(6) =30
• So 50 % now is 30, thus after discount price will be 60 + 30 = Rs90.
• Thus for 1000 -> 90(1000/100) = Rs900 Answer

Now try to Solve the same Question yourself, with 25% increase and 25% decrease.

It was quiet obvious to think that answer will be 100 but its not.

• First we calculate 25% of 100, which will be 25. So new amount is 125.
• Now we will calculate 25% dec in 125. For which we will do following –
  • Calculate 10% of 125 = 12.5, thus 20% is 2(12.5) = 25
  • Here rather than calculating 1% and multiply by 5 its better to divide 10%/2 to calculate 5%. Thus 6.25 is 5%
  • So total is 25 + 6.25 = 31.25 and value 93.25
  • Now price = 93.25(1000/100) = 932.5Rs.

There is no direct formula for such kind of problems.