CLASS-8
PROBLEM & 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.)