**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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