A man spends 2/5 of his income on house rent, 3/10 on food and 1/8 on conveyance. If he has ? 2800 left with him, find his expenditure on food and conveyance together.

Let first, second and third numbers be x , y and z, respectively.
Then , xy = 42.................(i)
yz = 56 ..................(ii)
xz = 48 ....................(iii)
Multiplying Eqs ( i), (ii) and (iii), we get
(xyz)² = 42 x 56 x 48
? (xyz)² = 112896
? xyz = 336 ................(iv)
Dividing Eq. (iv) by Eq. (i), we get
xyz/xy = 336/42 ? z = 8

Let the ten's place digit = x
and unit's place digit = y
? The original number = 10x + y
After interchanging the digits
Number will become 10y + x
? according to the given question,
y + x = 13 and
(10y + x ) - (10x + y) = 27
? 9y - 9x = 27
? y - x = 3 ................(i)
and y + x = 13 .................(ii)
On solving Eqs.(i) and (ii) , we get
y = 8 and x = 5
? Required number is
10x + y = 10 x 5 + 8 = 58

Let x bottles can fill the container completely.
According to the questions,
4/5 x - 3/4 x = (12 - 8)
? 16x - 15x/20 = (12 - 8)
? x/20 = 4
? x = 80
? Required number of bottles = 80.

Let Rahul's marks in Mathematics = x
and in Hindi = y
According to the question,
1/3 x - 1/2y = 30
? 2x - 3y = 180 ...(i)
Also, given
x + y = 480 ...(ii)
By solving Eqs. (i) and (ii), we get
x = 324
and y =156

Let the maximum marks = x.
According to the question,
40x/100 = 200 + 8
? x = 208 x 10/4 = 520

Let share of each friend = a.
Then, share of each daughter = 4a.
and share of each son = 5a.
According to the question,
5 x 5a + 4 x 4a + 2 x a = 17200
? 25x + 16x + 2x = 17200
? 43x = 17200
? x = 17200/43 = 400
? Share of each daughter
= 4x = 4 x 400
= ? 1600

Let at present, there are c men, then number of women = 5c
Before the men had left
number of men = c + 45 and
number of women = 5c
? c + 45 = 2 x 5c
? 9c = 45
? c = 45/9 = 5
Hence, number of women in the beginning
= 5c + 15 = 5 x 5 + 15
= 25 + 15 = 40
? Double of the women = 40 x 2 = 80

Adult fare = ? 114
According to the question,
child fare = Adult fare x 1/6
= 144 x 1/6 = ? 19
? Total amount paid by 4 adults and 5 children are for the same distance.
= ?(4 x 144 + 5 x 19)
= ?(456 + 95) = ? 551

Let the cost of 1 pencil = x
? Cost of 1 pen = (x + 5)
According to the question,
12(x + 5) + 5x = 111
? 12x + 60 + 5x = 111
? 17x = 111 - 60 = 51
? x = 51/17 = 3
? Cost of 1 pencil = ? 3
Cost of 1 pen = ? 8
? Total Cost of 8 pens and 9 pencils
= (8 x 8 + 9 x 3)
= ?(64 + 27) = ? 91

Let the total amount = x
According to the question.
14 girls are getting x amount.
1 girl will get x/14 amount.
Similarly if
18 girls are getting x amount.
1 girl will get x/18 amount.
according to question,
x/14 - x/18 = 160
? (9x - 7x)/126 = 160
? 2x/126 = 160
? x/126 = 80
? x = 126 x 80 = ? 10080