Profit, Loss and Simple Interest

Subject: Compulsory Maths

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Overview

When the selling price of a good is higher than its cost then, it is called profit. Similarly, when the selling price of goods is lower than its cost price then it is called loss. When there is an investment on Rs. 1000 and the C.P are considered as Rs. 100 and profit or loss is calculated on it, then it is called profit or loss percent. When a marked price of (M.P) of any article reduces and sells to the customer by shopkeeper then the reduced amount is called the discount. When a shopkeeper allows discount from Marked Price (M.P) of any article. When M.P is considered as Rs. 1000 and discount are calculated from it, then it is called Discount percent. Value added tax is a tax charged on the actual selling price of goods. Simple interest is the interest which is payable on the principal.
Profit, Loss and Simple Interest

Profit and Loss

source: passyworldofmathematics.com Fig: Profit and Loss
source: passyworldofmathematics.com
Fig: Profit and Loss

When the selling price of a good is higher than its cost then, it is called profit. In this case, profit is calculated as the difference between the selling price and the cost price.

Profit S.P - C.P
S.P C.P + profit
C.P S.P - profit

Similarly, when the selling price of goods is lower than its cost price then it is called loss. The loss is calculated as the difference between the cost price and the selling price.

Loss C.P - S.P
C.P S.P + loss
S.P C.P- loss

Profit and Loss percent

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When there is an investment on Rs. 1000 and the C.P are considered as Rs. 100 and profit or loss is calculated on it, then it is called profit or loss percent. For example,

The cost price of an article is Rs. 250 and it is sold at a profit of Rs. 100.

Here, On C.P of Rs. 250, Profit is of Rs. 100.

On CP Rs.1, Profit is Rs. \(\frac{100}{250}\)

On CP of Rs. 100, profitis Rs.\(\frac{100}{250}\) × 100 = Rs.40

∴ On CP of RS. 100, Profit is Rs. 40. So it is called 40% on profit.

The formulaes for Profit and the loss percent are

  1. Profit percent =\(\frac{profit}{C.P}\) × 100% or\(\frac{S.P - C.P}{C.P}\) × 100%
  2. Loss percent =\(\frac{Loss}{C.P}\) × 100% or\(\frac{C.P - S.P}{C.P}\) × 100%

Calculation of S.P when C.P and profit or loss percent are given

For this case, firstafall it needs to find actual profit and actual loss from C.P

  1. Actual profit = Profit percent× C.P
  2. Actual Loss = Loss percent× C.P

So, we can calculate S.P as

  1. S.P = C.P + Actual profit
  2. S.P = C.P - Actual loss

For example,C.P - Rs. 150 and profit percent is 15%. Find S.P.

Here, Actual profit = 15 % of C.P =\(\frac{15}{100}\) × Rs.150 = 22.5

Now, S.P = C.P + profit = Rs. 150 + 22.5 = 172.5 ans.

Calculation of C.P when S.P and profit or loss percent are given

For this case, the unknown value of C.P is considered as a variable such as x. Then the process of calculation will be as shown in the following example,

If the S.P = Rs. 250 and loss percent is 10 %, find C.P.

Here, Actual loss = 10% of C.P

or, \(\frac{10}{100}\) ×x =\(\frac{x}{10}\)

Now, C.P = S.P + loss

or, x = Rs. 250 + Rs. \(\frac{x}{10}\)

or, x -\(\frac{x}{10}\) = Rs. 250

or, \(\frac{9x}{10}\) = Rs. 250

or, x =\(\frac{Rs.250 × 10}{9}\)

= Rs. 277.78

∴ C.P = Rs. 277.78 ans.

Discount

source: passyworldofmathematics.com Fig: Discount
source: passyworldofmathematics.com
Fig: Discount

When a marked price of (M.P) of any article reduces and sells to the customer by shopkeeper then the reduced amount is called the discount.For example,

The marked price of a book is 125 and the shopkeeper reduces the Marked Price by 25. In this case, S.P of book = 125 - 25 = Rs.100.

  1. Thus S.P = M.P - Discount
  2. And Discount = M.P - S.P

Discount Percent

When a shopkeeper allows discount from Marked Price (M.P) of any article. When M.P is considered as Rs. 1000 and discount are calculated from it, then it is called Discount percent. It can be calculated by following formulas,

  1. Discount Percent = \(\frac{Discount}{M.P}\)× 100%
  2. Discount Amount = Discount percent of M.P

Value Added Tax (VAT)

source: www.authorstream.com Fig: VAT
source: www.authorstream.com
Fig: VAT

Value added tax is a tax charged on the actual selling price of goods. So, VAT is charged at a certain percent of S.P.

  1. VAT amount = VAT percent of S.P
  2. S.P with VAT = S.P + VAT percent of S.P

Simple Interest

source: passyworldofmathematics.com Fig: Simple Interest
source: passyworldofmathematics.com
Fig: Simple Interest

Generally, simple interest is the interest which is payable on the principal. When we deposit money in the bank for a certain time the bank will pay us some additional amount of money under a certain condition. Such additional amount of money is called interest.

Calculation of Simple Interest

The following terms appear in the calculation of simple interest,

  1. Principal (P)
  2. Rate (R)
  3. Time (T)
  4. Amount (A)

The formulae for calculating the Simple Interest,

I = \(\frac{P.T.R}{100}\)

Again, If I =I = \(\frac{P.T.R}{100}\)

P× T× R = I× 100

P = \(\frac{I× 100}{T × R}\)

T = \(\frac{I × 100}{P × R}\)

R = \(\frac{I × 100}{P × T}\)

Further more, when Amount (A) is the sum Principal (P) and its Intrest (I)

  1. A = P + I
  2. P = A - I
  3. I = A - P
Things to remember
  1. Profit S.P - C.P
    S.P C.P + profit
    C.P S.P - profit
  2. Loss C.P - S.P
    C.P S.P + loss
    S.P C.P- loss
  3. Profit percent =\(\frac{profit}{C.P}\) × 100% or\(\frac{S.P - C.P}{C.P}\) × 100%
  4. Loss percent =\(\frac{Loss}{C.P}\) × 100% or\(\frac{C.P - S.P}{C.P}\) × 100%
  5. Actual profit = Profit percent× C.P
  6. Actual Loss = Loss percent× C.P
  7. S.P = C.P + Actual profit
  8. S.P = C.P - Actual loss
  9. S.P = M.P - Discount
  10. Discount = M.P - S.P
  11. Discount Percent = \(\frac{Discount}{M.P}\)× 100%
  12. Discount Amount = Discount percent of M.P
  13. VAT amount = VAT percent of S.P
  14. S.P with VAT = S.P + VAT percent of S.P
  15. I = \(\frac{P.T.R}{100}\)

    Again, If I = I = \(\frac{P.T.R}{100}\)

    P × T × R = I × 100

    P = \(\frac{I× 100}{T × R}\)

    T = \(\frac{I × 100}{P × R}\)

    R = \(\frac{I × 100}{P × T}\)

    Further more, when Amount (A) is the sum Principal (P) and its Intrest (I)

    1. A = P + I
    2. P = A - I
    3. I = A - P 
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Questions and Answers

Solution:

Let, the required C..P. be Rs x,
Here,
Actual loss = 20% of C.P
= \(\frac{20}{100}\) × Rs x
= \(\frac{x}{5}\)
Now, 
C.P. = S.P. + loss
or, x = Rs 240 + Rs \(\frac{x}{5}\) 
or, x - \(\frac{x}{5}\) = Rs 240 
or, \(\frac{4x}{5}\) = Rs 240
or, x = \(\frac{5 × Rs 240}{4}\) 
or, x = Rs 300
So, the required C.P is Rs 300.

Solution:

Here,
C.P. of the watch = Rs 350 
S.P. of the watch = Rs 378 
∴ Profit = S.P. - C.P. = Rs 378 - Rs 350 
= Rs 28
Now,
profit percent = \(\frac{profit}{C.P.}\) × 100% 
= \(\frac{28}{350}\) × 100% 
= 8%
So, the required profit percent is 8%.

Solution:

Here,
the remaining number of glass tumblers = 100 - 10 = 90
C.P. of 100 glass tumblers = 100 × Rs 15 = Rs 1500 
S.P. of 90 glass tumblers = 90 × Rs 16 = Rs 1440
∴ Loss = C.P. - S.P.  = Rs 1500 - Rs 1440 = Rs 60
Now,
loss percent = \(\frac{loss}{C.P}\) × 100%
= \(\frac{Rs 60}{Rs 1500}\) × 100% 
= 4 %
So, his loss percentage is 4%

Solution:

Here,
S.P. of the radio = Rs 336 
Profit percent = 5% 
Let, the C.P. of the radio be Rs x.
Now, 
Actual profit = 5% of C.P.
= \(\frac{5}{100}\) × Rs x 
= Rs \(\frac{x}{20}\)
Again, 
or, C.P. = S.P. - profit 
or,  x = Rs 336 - \(\frac{x}{20}\) 
or, x + \(\frac{x}{20}\) = Rs 336 
or, \(\frac{21x}{20}\) = Rs 336
or, x = \(\frac{20 × Rs 336}{21}\) 
or, x = 320
So, he purchased the radio for Rs 320

Solution:

Here,
M.P. of the article = rs 450 
S.P. of the article = Rs 405 
∴ Discount = M.P - S.P = Rs 450 - Rs 405
= Rs 45
Now, 
Discount percentage = \(\frac{Discount}{M.P}\) × 100% 
= \(\frac{rs 45}{Rs 450}\) × 100% 
= 10%
So, the required discount percentage is 10%

Solution:

Here,
M.P of the radio = Rs 960
Discount percent = 5% 
∴ Discount amount = 5% of M.P
= \(\frac{5}{100}\) × Rs 960
= Rs 48 

Solution:

Here,
M.P. of the camera = Rs 1800 
Discount percent = 10%
VAT percent = 10%
Now,
discount amount = 10% of M.P 
= \(\frac{10}{100}\) × Rs 960 
= Rs 180
∴ S.P = M.P - Discount = Rs 1800 - Rs 180
= Rs 1620
Again,
VAT amount = 10%  of S.P
= \(\frac{10}{100}\) × Rs 1620 
= Rs 162
∴ S.P with VAT = S.P + VAT amount 
= RS 1620 + Rs 162
Rs 1833
So, the customer pays Rs 1822.

Solution:

Here,
C.P. of the bicycle = Rs 1200 
∴ M.P, of the bicycle = Rs 1200 + 20% of Rs 1200
= Rs 1200 + \(\frac{12}{100}\) × Rs 1200 
= Rs 1200 + Rs 240 
= Rs 1440
Now,
Discount amount = 10% of M.P = \(\frac{10}{100}\) × Rs 1440 
= Rs 144
∴ S.P = M.P. - Discount amount = Rs 1440 - Rs 144 
= Rs 1296 
Again,
VAT amount = 10% of S.P 
= \(\frac{10}{100}\) × Rs 1296 
= Rs 129.60
∴ S.P. with VAT = S.P. + VAT amount 
= Rs 1296 + Rs 129.60
= Rs 1425.60
So, the customer should pay Rs 1425.60

Solution:

Here,
Principle (P) = Rs 2500 
Rate (R) = 7% per year 
Time (T) = 5 years
Now,
Interest (I) = \(\frac{P × T × R}{100}\) 
= Rs \(\frac{2500 × 5 × 7}{100}\) 
= Rs 875
Again,
Amount (A) = P + I 
= Rs 2500 + Rs 875 
= Rs 3375
So, she received an amount of Rs 3375.

Solution:

Here,
Principle (P) = Rs 3600 
Amount (A) = Rs 5328
Rate (R) = 12% per year 
Now,
Interest (I) = A - P 
= Rs 5328 - Rs 3600
Rs 1728
Again,
Time (T) = \(\frac{I × 100}{P × R}\) 
= \(\frac{1728 × 100}{3600 × 12}\) 
= 4 years 
So, the required time is 4 years.

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