SOLVING WORD PROBLEMS INVOLVING FRACTIONS

Problem 1 :

A man spends 2/5 of his salary on house rent, 3/10 of his salary on food and 1/8 of his salary on conveyance. If he has $1400 left with him, find his expenditure on food and conveyance.

Solution :

Let 1 be the whole part of salary.

Part of the salary left over  =  1 - [(2/5) + (3/10) + (1/8)]

  =  1 - [(16+12+5)/40]

  =  1 - (33/40)

  =  7/40

Amount left over in his salary  =  1400

Let x be his salary.

7/40 of x  =  1400

x  =  1400 (40/7)

x  =  8000

For food he is spending 3/10 of his salary.

Amount spend for food  =  3/10 of 8000

  =  $2400

Amount spend for conveyance  =  1/8 of 8000

  =  $1000

Problem 2 :

A third of Arun's marks in mathematics exceeds a half of his marks in English by 30. If he got 240 marks in the two subjects together, how many marks did he get in English ?

Solution :

Let x and y be the marks in the subject Math and English respectively.

(x/3)  =  (y/2) + 30

(x/3) - (y/2)  =  30 -----(1)

x + y  =  240

y  =  240 - x  ----(2)

Apply (2) in (1), we get

(x/3) - [(240 - x)/2]  =  30

[2x - 3(240 - x)]/6  =  30

2x - 720 + 3x  =  180

5x - 720  =  180

5x  =  900

x  =  180

By applying the value of x in (1), we get

y  =  240 - 180

y  =  60

So, the marks scored in the subjects math and English are 180 and 60.

Problem 3 :

If 1/8 of a pencil is black, 1/2 of the remaining is white and the remaining 3  1/2 cm is blue, find the total length of the pencil.

Solution :

Let x cm be the length of pencil.

(1/8) of x  ==>  x/8  =  Black   

length of remaining part of pencil  =  x - x/8  =  7x/8

(1/2) of (7x/8)  =  white

7x/16  =  white

length of pencil colored blue  =  3  1/2  ==>  7/2

(x/8) + (7x/16) + 7/2  =  x

(2x + 7x + 56)/16  =  x

9x + 56  =  16x

56  =  7x

x  =  56/7

x  =  8 cm

So, the length of the pencil is 8 cm.

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