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.)