Chapter - 11
PERCENTAGE AND ITS APPLICATIONS
‘Per cent’ means ‘out of one hundred’. Symbol % is used to denote per cent
Some examples to convert a per cent into a fraction, ratio or decimal and vice versa.
6) (i) 50% = 0.50
(ii) 7% = 0.07
(iii) 90% = = 0.90
(iv) 1% = 0.01
8) (i) 10% of 100 = 10
(ii) 20% of 500 = 100
(iii) 30% of 1000 = 300
9) (i) 5 out of 25 = 20%
(ii) Re 1 out of Rs 25 = 4%
(iii) 10 out of 50 = 20%
(i) If 25% of X= 30 find X
Sol. 25% of X is and it is equal to 30
(ii) If 4.6% of X is 23 find X
Sol. 4.6% of X means and it is given to be equal to 23
So = 23
or X =
(iii) If 24% of X is 48, then find x
Sol. 24% of X is 48
Example 2: Vijay deposits Rs 45 per month in the bank. If this amount is 15% of his monthly income, find his monthly income.
Solution: Let his monthly income be Rs X
As per the given statement 15% of X is 45
or x = = 300 RS
Example 3: Gunpowder contains 75% nitre and 10% sulphur. The rest of the material is charcoal. Find the amount of each of the contents in 9 kg of gunpowder.
Solution: Weight of gunpowder = 9 kg
Contents are – nitre = 75%, Sulphur = 10% charcoal = 100-75-10 = 15%
Nitre in 9 kg = = 6.75 kg.
Sulphur in 9 kg = = 0.90 kg.
Charcoal in 9 kg = = 1.35 kg.
Example 4: Priya got 87.5% marks in the annual examination. If she got 700 marks, find the total number of marks in the examination.
Solution: Let total marks be X
A per the statement 87.5% of X = 700
So total marks = 800
Example 5: The value of a machine depreciates by 10% every year. If its present value is Rs 38700, what was its value one year ago.
Solution: Let the value last year be x
If it is decreased by 10% the present value will be
and as per the given statement
or x = = 4300 X 10 = Rs. 43000.
Example 6: The salary of a person has been increased by 25%. By what per cent should the salary be reduced so that he gets the original salary.
Solution: Let original salary be 100
Salary after an increase of 25% = 100+25=125
To restore the salary back to 100 it should be decreased by Rs 25
The reduction on 125 = Rs 25
The reduction on 100 =
Example 7: Ankits salary is 25% more than that of Anil. What percent is Anil’s salary less than Ankits?
Solution: Let Anil’s salary be Rs 100
Then Ankit gets 25% more than Anil = 125
Now If Ankit’s salary is Rs 125 Anil’s = 100.
If Ankit’s salary is Rs 100 then Anil’s =
So Anils salary is Rs 80 when Ankit’s is Rs 100
So Anil salary is 20% less than Ankit
Example 8: Raman loses 20% of his money. After spending 25% of the remaining, he has Rs 480. How much did he originally had?
Solution: Suppose Raman had Rs 100 in the beginning. He lost 20% i.e. Rs. 20
Remainder = Rs 100 – Rs 20 = Rs 80
Out of Rs 80 he spent 25%, which is equal to
Remainder = Rs 80 – Rs 20 = Rs 60
If remainder is Rs 60, he originally had = Rs 100
If remainder is Rs1, he originally had =
If remainder is Rs 480 he originally had =
Example 9: The price of wheat increases by 10%. By what per cent should a consumer reduce his consumption so that his expenditure of wheat remains the same.
Solution: Let the original consumption of wheat is 100 kg and the price is Rs 100 per kg.
Expenditure originally = Rs 100 x 100
Expenditure now if consumption is X kg @ Rs 110 per kg = x X 110 Rs
But the expenditure remains to be the same
So x X 110 = 100 X 100
So reduction in consumption =
Example 10: The price of a shirt in Dec 1997 was Rs 250. In Jan. 1998 it was increased by 10% and in Oct 1998 it was reduced by 10%. What in the new price of the shirt.
Solution: Price in Dec 1997 = Rs 250
Price in Jan 1998 =
Price in Oct 1998 = 275 x = Rs 247.50
Example 11: In an examination a candidate must secure 40% marks to pass. A candidate got 220 marks and failed by 20 marks. What are the maximum marks for the examination.
Solution: Let the maximum marks be x
Marks required to pass =
As per the statement the marks required to pass = 220 +20 = 240 ------- (ii)
So from I and II
Example 12: When 75% of a number is added to 75, the result is the same number. Find the number.
Solution: Let the number be x
As per the given statement.
75% of X + 75 = x