# CLASS-8PROBLEM & SOLUTION OF FRACTION

PROBLEM & SOLUTION OF FRACTION

Example.1) Jack has a packet of 20 balls, he gave ¼ to Frank and  1/5 of the remaining to Harry, of the rest he gave  1/3 of the remaining to Richard. Find the number of balls finally left with Jack. what fraction of the packet was left with him ?

Answer.) As per the given condition, Frank got a number of balls                                         1

=    20  X ------- =  5 balls

4

So, remaining balls  = 20 – 5 = 15

1

Harry received number of balls = 15 X ------  = 3 balls

5

Remaining balls = 15 – 3 = 12 balls

1

Richard received number of balls = 12 X ------ =  4 balls

3

Remaining balls  =  12 -  4  =  8

As per the given condition, the required fraction is  =

8             2

--------- = --------       (Ans.)

20             5

Example-2) 8/15 of a number exceeds 4/25 of the number by 140, find the number.

Answer)  Let the required number is  z

As per the given condition if one number is 8z / 15, then another would be 4z / 25, so according to that condition

8z              4z

---------- - ---------  = 140

15              25

( 8z X 5 )  -  ( 4z X 3 )

=>  ---------------------------  =  140

75

40z – 12z

=>  ---------------  =  140

75

=>     28 z  =   140 X  75

140 X 75

=>   z   =  -----------------  =  5 X 75 =  375

28

So, the required number is  375  (Ans.)

Example.-3) Richard’s monthly salary is \$ 3500, he pays 1/10 of his salary as tax and spends 7/45 of the remaining on the education of his children. 1/5 of the rest is paid as the rent of the house and \$1000 is spent on food & conveyance. Find Richard’s monthly savings.

1

Answer)  The amount paid as Tax = ------- X  3500 =  350

10

The remaining amount = \$ 3500 - \$ 350 =  \$ 3150

7

Amount spent on Children’s education =  3150 X -------

45

=    \$ 490

Remaining amount is = \$ 3150 - \$ 490 = \$ 2660

Now he spend as house rent 1/5 of the rest amount, so the rent amount is =

1

=  \$ 2660 X --------   =  \$ 532

5

Remaining amount = \$ 2660 - \$ 532 =  \$ 2128

He spent \$1000 on food & conveyance  =  \$ 2128 - \$1000

= \$ 1128

Hence, Richard’s monthly savings is  \$ 1128.  (Ans.)

Example.4)  If 3/20 of a number is less than 7/10 of the number by 110, then find the number.

Answer)   Let the required number is  x

As per the given condition if one number is 3x / 20, then another would be 7x / 10, so according to that condition

7x                3x

----------  -  ---------  =  110

10                20

( 7x X 2 )  -  ( 3x X 1 )

=>  -----------------------------  =  110

20

14x – 3x

=>   -------------  =  110

20

=>       11 x  =   110 X  20

110 X 20

=>  x   =  -------------

11

x   =   10 X 20  =  200

So, the required number is  200   (Ans.)