Tips and Tricks for Profit/Loss and discount

Discount is defined as the amount of rebate given on a fixed price (called as marked price) of an article. It is given by merchants/ shopkeepers to increase their sales by attracting customers.
Discount = Marked Price - Selling Price

Marked Price (List Price)(MP) :The price on the label of an article/product is called the marked price or list price.

1. Profit percentage (P%) = (Profit /Cost Price) × 100

2. Loss percentage (L%) = (Loss / Cost price) × 100

3. S.P. = {(100 + P%) / 100} × CP (if SP > CP)

4. S.P. = {(100 – L%) / 100} × CP (if SP < CP)

5. C.P. = {100 / (100 + P%)} × SP (if SP > CP)

6. C.P. = {100 / (100 – L%)} × SP (if SP < CP)

Note Discount is always calculated with respect to marked price of an article

 

Points worth noting :

• MP is always marked up on CP
• Discount is always allowed on MP
• Gain or Loss is always represented as percentage of CP unless stated otherwise
• Common mistake made by students is calculating gain percentage on SP.

 

Type 1: Successive Discount

When a series of discounts (one after the other) are allowed on marked price of an article, then these discounts are called successive discounts.

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)%

Qustion 1: 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)  = Rs - 720

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%

Qustion 2: 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 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 ?

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 a better deal.

Type-2: Find CP,SP,MP

Question-3: MRP of an item is 800 Rs. If a discount of 15% is given on its marked price. Then the Selling price of item is ?

Solution:

MRP=800
Discount=15%

SP=(100-15)/100 x 800=680Rs.

Type 3:

Question 4: Buy 3 get 3 free . Calculate discount % ?

Solution: Let's say price for one piece is x

For 3 piece = 3x

For 4 piece = 6x

Here you are getting products of price 6x in price of 3x

So discount percentage is

(discount / original price ) ×100

Here discount= (original price - discounted price )

=(6x-3x)

Discount percentage=( 3x/6x ) ×100 = 50%           

Question 5:   Buy 5 get 4 free + 20 % more discount. Calculate net discount %.

Solution: Let's say price for one piece is x

For 5 piece = 5x

For 9 piece = 9x

Discount=20%

Net Price=5x *80/100 = 4x

Here you are getting products of price 9x in price of 4x

So discount percentage is

(discount / original price ) ×100

Here discount= (original price - discounted price )

=(9x-4x)=5x
Discount percentage=( 5x/9x ) ×100 = 55 1/9%

Type 4:(If discount% and Profit% given)

Question: 6 The marked price of a bicycle is Rs 1100. A shopkeeper allows a discount of 10% and get a profit of 10%. Find the cost price of the bicycle ?

Solution1 : M.P. of cycle = Rs. 1100

After Discount S.P = 90% of 1100 = Rs. 990 gain = 10%

C.P. = 990×100/(100+10)

=  990×100/110= Rs.900

Solution 2: Ratio Method

Discount=10%=1/10

So Ratio of SP and MP=9:10

Profit=10%=1/10

So Ratio of CP and SP=10:11

So CP:SP:MP=90:99:110

Given that MP=1100

110 will be =1100

1 will be =10

90 will be =10x90=900

Ratio method is very Important and can be used to solve all type of question based on Discount

Question 7: A shopkeeper allows 25% discount on mark price and earn 30% profit . If he gets Rs 90 as profit. Find the amount of the discount ?

Solution 1:

Profit = 30% = 90 Rs.

So cost price - 90/30*100 = 300

And Selling Price = 300+90 = 390

Discount = 25% of marked price

So sales price = (100-25)% = 75 % of marked price therefore, 390 = 75% of marked price

marked price = 390/75*100 = 520 Rs.

Discount = 25% of marked price

Discount = 25/100*520 = 130 Rs.

Solution 2: (Ratio Method)

Discount=25%=1/4

So Ratio of SP and MP=3:4

Profit=30%=3/10

So Ratio of CP and SP=10:13

So CP:SP:MP=30:39:52

Given that Profit=90

9 will be =90

1 will be =10

13 will be =10x13=130

Type 5:(Marked up CP)

Question 8:

A shopkeeper marks his good 20% higher than the cost price and allow a discount of 5%. What is the percentage of his profit ?

Solution1: Let CP be Rs 100, then MP=Rs 120

Discount is always given on MP and after discount MP becomes SP

So, SP=95/100×120= Rs 114

Therefore, profit =114-100=14 and p%=14%

Solution-2:

By Applying  Successive Formula

P%=profit %
MP%= Marked up on CP
D%=Discount %

P%=MP% - D%-(MP xD)/100

P%=20-5-(20x5)/100=14%