The document consists of various mathematical problems focused on percentages, including calculations of percentage change in savings, errors in calculations, and population growth. It includes example problems and their solutions, demonstrating various percentage concepts and their applications. The document serves as a resource for practice on percentage-related problems.

1. Percentage - 2

2. change = 100
error = 100
• A = x % of B => if B = 100 then A = x
• A = x % more than B => if B = 100 then A = 100 + x
• A = x % less than B => if B = 100 then A = 100 – x
• 100 % of any value is value itself.
Basics :
COMSCIGUIDE

3. 1. A man is saving 33 of his income. If his income is increased by 25% and
expenditure is increased by 40%, then what is the % change in his savings?
2. A student by mistake multiplied a number with instead of multiplying with .
What is the % error in calculation?
3. The population of a town is increasing by 20% every year. If the present
population of town is 72000, then what is the population of the town 2 years ago
?
4. The price of the sugar is decreased by 30%. What is the % change in
expenditure if consumption is increased by 40% ?
5. In an examination, A boy scores 31% of max marks and fails by 12 marks. A girl
scores 45%of max marks and pass by 16 marks. Find the max marks and the
% required to pass?
COMSCIGUIDE

4. 1. A man is saving 25% of his income. If his income is increased by 20%
and expenditure is increased by 10%, then what is the % change in
his savings?
Ans :
income = savings + expenditure
100 25 75
120 37.5 82.5
% change = 100
= 50%
100 % = 75
10% = 7.5
% change in his savings = 50%
COMSCIGUIDE

5. A student by mistake multiplied a number with instead of
multiplying with . What is the % error in calculation?
2.
Let take a number which is multiplied by both numbers
i.e. the lcm of two denominators. => lcm of (4,5) = 20
=> % error = 100
= 36%
% error = 100
= 36%
Ans : 20 = 16
20 = 25
25 --- 16
100 --- 64
36%
% error in calculation = 36% COMSCIGUIDE

6. A student by mistake divided a number with instead of
multiplying with 2. What is the % error in calculation?
2.
First convert both operations into one format ,the
operation that we have to do on the number. Here it is
multiplication.
=> % error = 100
= 75%
% error = 100
= 75%
Ans :
4 --- 1
100 --- 25
75%
% error in calculation = 75% COMSCIGUIDE

7. The population of a town is increasing by 20% every year. If the
present population of town is 72000, then what is the population of
the town 2 years ago ?
3.
The population of the town is increasing every year. Before 2
years it is less than the present population.
 the percentage improvement is 20 %
i.e one year later it will be present population
Similarly the population after 2 years will be present population
Therefore 2 years ago the population will be present population
Population 2 years ago = 72000 = 50,000
Ans :
Population of the town 2 years ago = 50,000COMSCIGUIDE

8. The price of the sugar is decreased by 30%. What is the % change in
expenditure if consumption is increased by 40% ?
4.
Expenditure = consumption price
10000 100 100
9800 140 70
Ans :
100 = 2%
Method - 2
Method - 1
100 140 98
2% decrease
40 42
For method -2 assume initial amount as 100
% change in expenditure = 2%
COMSCIGUIDE

9. In an examination, A boy scores 31% of max marks and fails by 12
marks. A girl scores 45%of max marks and pass by 16 marks. Find the
max marks and the % required to pass?
5.
Ans :
Maximum marks = 200
% Required to pass = 37%
Max marks boys girls
100 31 45
 14% = 28 marks
 1% = 2 marks
 100% = 200 marks = maximum marks
 12 marks = 6% and already boy has 31%
 31+6 = 37%
%required to pass is 37
COMSCIGUIDE

10. Subscribe to :
Problems for practice are given in the description of the video.
COMSCIGUIDE

11. Practice problems
on Percentages

12. 1. A train crosses a pole in 12 sec. It crosses a bridge of length 300m in 27
sec. what is the time taken by the train to cross a bridge of length of 600m?
2. A train crosses a bridge of length 122m in 17 sec. it crossed another bridge
of length 210m in 25 sec. find the length of the train?
3. A train travelling at a speed of 54kmph crosses a platform in 36 sec and a
man standing on the platform in 20 sec. find the length of the platform?
4. A train of length 240m travelling at a speed of 64kmph overtakes a man
running at a speed of 10 kmph in __ sec ?
5. A train starts from a station X at 6am and reaches another station Y at 10
am. Another train starts from station Y at 8am and reaches station ‘X’ at
11:30am. At what time do the trains cross each other?
COMSCIGUIDE

13. The price of the sugar is increased by 25%. What is the % change in
consumption, if expenditure is increased by 50% ?
4.
Ans :
100 125 150
50% increase
25% x%
For method -2 assume initial amount as 100
100 = 20%
% change in consumption = 20%
COMSCIGUIDE

14. The value of a machine is decreases by 30% every year. If the
present value of a machine is 1,47,000, then what is the value of the
machine 2 years ago?
3.
The value of a machine before 2 years will be present price
Value of a machine 2 years ago = 1,47,000 = 3,00,000
Ans :
Value of the machine 2 years ago = 3,00,000
COMSCIGUIDE

15. A student by mistake multiplied a number with instead of
dividing with 3. What is the % error in calculation?
2.
First convert both operations into one format ,the
operation that we have to do on the number. Here it is
multiplication.
=>
% error = 100
= -800%
Ans :
9 --- 1
900 --- 100
-800% error in calculation = 800%
COMSCIGUIDE

16. A student by mistake multiplied a number with instead of dividing
with . What is the % error in calculation?
2.
 Error in calculation is zero
 Since multiplying with 2/5 is equal to dividing with 5/2
Ans :
% error in calculation = 0%
COMSCIGUIDE

17. Subscribe to :
COMSCIGUIDE