Subject: Compulsory Maths
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
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
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
So, we can calculate S.P as
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
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.
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,
Value Added Tax (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.
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,
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)
Profit | S.P - C.P |
S.P | C.P + profit |
C.P | S.P - profit |
Loss | C.P - S.P |
C.P | S.P + loss |
S.P | C.P- loss |
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)
If S.P = Rs 240 and loss percent is 20%, find the C.P.
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.
A shopkeeper buys a watch for rs 350 and sells it for 378. Find his profit percentage.
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%.
Kedar bought 100 glass tumblers at the rate of Rs 15 each. 10 of them were broken and he sold the remaining at rate of Rs 16 each. find his profit or loss percent.
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%
A shopkeeper sold a radio for Rs 336 at 5% profit. At what price did he purchase the radio?
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
The marked price of an article is Rs 450. if the shopkeeper gives some discount and sells it for Rs 405, find the discount percentage.
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%
The marked price of a radio is Rs 960 and the retailer allows 5% discount to the customer. Find the discount amount.
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
The marked price of a camera is rs 1800. If the shopkeeper allows 10% discount, how much does a customer pay for it with 10% VAT?
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.
A man bought a bicycle for Rs 1200 and fixed its price 20% above its cost price. He then allows 10% discount. How much should a customer pay for it with 10% VAT?
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
Sunayana deposited a sum of Rs 2500 in a bank at the rate of 77% per year. Find the amount received by her at the end of 5 years.
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.
In how many years a sum of Rs 3600 amount to Rs 5328 at 12% per year simple interest?
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.
© 2019-20 Kullabs. All Rights Reserved.