# CLASS-8WORD PROBLEM & SOLUTION OF FRACTION

WORD PROBLEM & SOLUTION

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 number of balls =

1

20 X ------- =  5 balls

4

So, remaining balls =  20 – 5 = 15 balls

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 balls

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 of Children’s education =  3150 X -------- = \$ 490

45

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  =  --------------  =   10 X 20  =  200

11

So, the required number is  200     (Ans.)