# CLASS-8PERCENTAGE-PROBLEM & SOLUTION

PERCENTAGE - PROBLEM & SOLUTION

Example.1) If 50 increased by 30%, then find out the new number

Ans.)                      30

50 X  ---------- =  15

100

New number will be  =  50 + 15  =  65

Example.2) The price of the petrol decreased by 10% to \$ 50 per liter, find out the old price

Ans.)      As per the given condition

100 is decreased to 100 - 10 =  90

90

1 is decreased into  =  ----------

100

90

50 is decreased to =  50 X ---------- =  45

100

The old price is 45   (Ans.)

ALTERNATIVELY –

New quantity

Original quantity = -----------------------

x

( 1 +  --------- )

100

\$ 50

Original quantity = --------------------

10

( 1 + --------- )

100

\$ 50

= ------------ =  \$ 45.45  =  \$ 45  (Ans.)

11 / 10

Example.3) 3224 students appeared in an examination and 75% passed, how many failed ?

Ans.)  As per the situation, 75% of 3224 students has passed

75

So, number of passed student = ---------- X  3224

100

=    32.24 X 75  =  2418

Hence the number of students who failed  =  3224 – 2418

=  806

Alternative method –

Since, 75% passed, that’s mean 100 – 75 = 25 % failed.

25

So, number of student failed = --------- X 3224  students

100

=  806 students failed         (Ans.)

Example.4) Mr. Thomson gets a salary of \$ 4500 per month. His salary increases by 10% every year. Find (1) the increases in his (monthly) salary after a year, (2) his monthly salary after two years, and (3) his monthly salary after three years.

(1) the increases in his (monthly) salary after a year

Ans.) Mr. Thomson get a salary of \$ 4500 per month, if he get a 10% increment

Then, 1st year we will be getting increment

10

=   \$ 4500 X ---------   =   \$ 450                                                                                                                                              100

After 1st year his salary would be = \$ 4500 +  \$ 450

= \$ 4950 ………………. (1)  (Ans.)

10

In 2nd year his salary would be = \$ 4950 X ---------

100

=  \$ 495

After 2nd  year his salary would be = \$ 4950 +  \$ 495

= \$ 5445 ………………. (2)    (Ans.)

10

In 3rd  year his salary would be =  \$ 5445 X --------

100

=  \$ 544.5

After 3rd  year his salary would be = \$ 5445 + \$ 544.5

= \$ 5989.5 ……………….(3)   (Ans.)

Example.5)  A farmer takes 500 apples to the market. In the first hour, he sells 10% of the apples. In the second hour, he sells 15% of the remaining apples. Now the question arises –

1) How many apples does he sell?

2) How many apples are left with him after two hours?

3) What percentage of the total apples does he sell in two hours?

Ans.)  As per the given condition, a farmer takes 500 apples to the market.

In 1st hour he has sold out 10% of 500 apples, which is

10

=  500 X ---------- =  50                                                                                                                                                    100

So, remaining apples = 500 – 50 =  450 apples

In the 2nd hour he has sold out 10% of 450 apples, which is

10

=  450 X ----------  =   45                                                                                                                                                  100

Remaining apples =  450 – 45 =  405

So, total apple he has sold =  50 + 45

=  95 apples …………………… (1)  (Ans.)

He has left  500 –  ( 50 + 45 )

=  500 – 95 = 405 apples remains ………………… (2) (Ans.)

95

Percentage of apples he has sold out = --------- X 100

500

= 19% of apple he has sold in 2 hours………………(3)  (Ans.)

Example.6) Of the two candidates in an election, one got 35% of the votes and lost by 30345 votes. To find the total number of votes polled.

Ans.) As per the given condition, one candidate has got 35% of votes and lost by 30345

Suppose the total number of voters is Z

1st candidate has got 35% votes of Z, so he has got the votes

35Z

=  ------------                                                                                                                                                          100                                                                                                                   The 2nd candidate has got the 100 – 35

65Z

= 65 % votes, which is  -----------                                                                                                                                                          100

Now, as per the given condition

65Z           35Z

= --------- - --------- =  30345

100           100

30Z

Or, -----------  =  30345

100

Or,  30Z =  30345 X 100

30345 X 100

Or,  Z  =  -----------------  =  10115 X 10 =  101150

30

Total number of votes polled 101150   (Ans.)

Example.7) If Y’s income is 25% more than Z’s, by what percent is Z’s income less than Y’s income

Ans.)  Let, income of ‘Z’ is = \$ 100

And as per the given condition, income of ‘Y’ would be.

25

=  \$ 100 X  ----------  +  \$ 100                                                                                                                                                100

=  \$ 25 + \$ 100  =   \$ 125

So, Z’s income (\$100) is \$ 25 less than Y’s income (\$125)

25

The required percentage = ----------- X 100 =  20 %

125

Hence Z’s income is 20% less than Y’s income.       (Ans.)

Example.8) In an examination, 25% of the student failed in English, 35% failed in mathematics and 15% failed in both, find –

1) the percentage of students who failed in only English,

2) the percentage of students who failed in only mathematics

3) the percentage of students who failed in either one or both the subjects

4) the percentage of students who passed in both the subjects and

5) the total number of students, if 220 passed in both the subjects

Ans.)  Let the total number of students = 100

Then the number of students who failed in English = 25

Then, the number of students who failed in Mathematics = 35

Number of students who failed in both English & Mathematics = 15

So, the number of students who failed only in English

= 25 – 15 = 10 ………………………..(1)      (Ans.)

So, the number of students who failed only in Mathematics

= 35 – 15 = 20………………….(2)     (Ans.)

Now the total number of students who failed = the number of students who failed in only English + the number of students who failed in only mathematics + the number of students who failed in both English & Mathematics = 10 + 20 + 15 = 45

So, the percentage of students who failed in either one or both the subjects = 45…………………..(3)   (Ans.)

So, the total number of students who passed in both the subjects = total number of students – total number of students who failed = 100 – 45 = 55

Hence the percentage of students who passed in both subjects = 55 ………………………….(4)     (Ans.)

As per the condition, 220 students passed in both the subjects

So,  55% of the students  =  220

55

So, the total number of students = 220 ÷  ----------

100

100

=  220 X ----------  =  400 students………………(5)  (Ans.)

55