Mani Ram divides ? 17200 among his 5 sons, 4 daughters and 2 friends. If each daughter receives four times as much as each friend receives and each son receives five times as mush as each friend receives, how much does each daughter receive?

Hint 1.
Let consider the monthly income = x ;
Amount spend on House rent = 2x/5;
Amount spend on food = 3x/10;
Amount spend on conveyance = x/8;
After Expenditure , The left amount = 2800;

According to Question;
x - ( 2x/5 + 3x/10 + x/8 ) = 2800 ;
x- ((16x + 12x + 5x)/40) = 2800 ;
x - 33x/40 = 2800 ;
(40x - 33x)40 = 2800 ;
7x/40 = 2800 ;
7x = 2800 x 40 ;
x = 2800 x 40/7 ;
x = 400 x 40 ;
x = 16000 ;
Expenditure on food = 3x/10 = 3 x 16000 /10= ? 4800
Expenditure on conveyance = x/8 = 1 x 16000/8 = ? 2000
? Expenditure on food and conveyance together
=? (4800 + 2000) = ? 6800



Solution 2 .

part of income left
= 1 - (2/5 + 3/10 + 1/8 )
=1- (16 + 12 + 5/40)
= 1- 33/40 = 40 - 33/40 = 7 /40
Let the monthly income = x
According to the question,
7/40 x = 2800
? x = 2800 x 40/7
= 400 x 40 = ? 16000
Expenditure on food = 3/10 x 16000 = ? 4800
Expenditure on conveyance = 1/8 x 16000 = ? 2000
? Expenditure on food and conveyance together
=? (4800 + 2000) = ? 6800

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 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

Solution 1 :
Let the number of ? 50 notes = x, then the number of ? 100 notes = (170 - x)
According to question.
50x + 100(170 - x) = 10000
divide by 50 the above equation, we will get
? x + 2(170 - x) = 200
? x + 340 - 2x = 200
? -x = 200 - 340 = -140
? x = 140
? Required amount ? 50 x 140
= ? 7000


Solution 2 :
Let the number of ? 50 notes = x and the number of ? 100 notes = y.
according to given question,
x + y = 170 .............(1)
50x + 100y = 10000............(2)

Divide the equation (2) by 10 , we will get
5x + 17y = 1000............(3)
Multiply the equation (1) by 5
5x + 5y = 850 ------------(4)
Subtract the (4) equation from (3) equation, we will get,
5x +10y - ( 5x + 5y ) = 1000 - 850
? 5x +10y - 5x - 5y = 1000 - 850
? 10y - 5y = 1000 - 850
? 5y = 150
? y = 150/5
? y = 30
Number of ? 100 notes = y = 30;
since x + Y = 170
therefore x = 170 - y
? x = 170 - 30
? x = 140
Number of ? 50 notes = x = 140