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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