The ratio of two numbers is 4:7. If each of those numbers increased by 30, their ratio will become 5:8 . What is the average of these two numbers?

Method 1
Let us assume the present age of mother be M and daughter be D.
According to question,
Ratio of present age of mother and daughter = 7 : 1
M / D = 7 : 1
? M / D = 7 / 1
? M / D = 7
? M = 7D ..........................(1)
Four years ago the age of mother = M - 4
Four years ago the age of daughter = D - 4
Again according to question,
Four years ago ratio of mother age and daughter age = 19 : 1
? (M - 4 ) / (D - 4) = 19 : 1
? (M - 4 ) / (D - 4) = 19
? (M - 4 ) = 19(D - 4)
? M - 4 = 19D - 76 .....................(2)
Put the value of M from equation (1) in above equation (2), we will get
7D - 4 = 19D - 76
? 76 - 4 = 19D - 7D
? 72 = 12D
? 12D = 72
? D = 72/12
? D = 6
Put the vale of D in equation (1), we will get the present age of mother.
Present age of Mother M = 7D = 7 x 6
Present age of Mother M = 42
? mother's age after 4 yrs = 42 + 4 = 46 yrs

Method 2
Let us assume the ratio factor is x.
According to question,
Ratio of present age of mother and daughter = 7 : 1
Then present age of mother = 7x and present age of daughter = x
Four years ago the age of mother = 7x - 4
Four years ago the age of daughter = x - 4
Again according to question,
Four years ago ratio of mother age and daughter age = 19 : 1
? (7x - 4 ) / (x - 4) = 19 : 1
? (7x - 4 ) / (x - 4) = 19
? (7x - 4 ) = 19(x - 4)
? 7x - 4 = 19x - 76
? 76 - 4 = 19x - 7x
? 72 = 12x
? 12x = 72
? x = 6
Present age of Mother = 7x = 7 x 6 = 42
? mother's age after 4 yrs = 42 + 4 = 46 yrs

Suppose that the Ravi present age is A years.
According to the given question,
A/4 + A/5 + A/3 + 13 = A
? (15A + 12A + 20A)/60 = A - 13
? 47A = 60A - 780
?60A - 47A = 780
?13A = 780
? A = 780/13 = 60 years

Let us assume the certain Number is A.
According to question,
63A = 3834 + 36A
63A - 36A = 3834
? 27A = 3834
? A = 142

Let us assume the digits of the original number are unit's digit a and ten's digit b.
The Original Number will be 10a + b.
After interchanging the digits the new number will be 10b + a.
According to question,
The number obtained by interchanging the two digits of a two-digit number is lesser than the original number by 54.
New Number = Original Number - 54
10b + a = 10a + b - 54
? 10b + a - 10a - b = -54
? 9b - 9a = -54
? a - b = 6....................................(1)
Again according to question,
Sum of the digits of original number = 10
a + b = 10..................................................(2)
Add the equation (1) and (2), we will get
a - b + a + b = 10 + 6
2a = 16
a = 8
Put the value of a in Equation (2) , we will get
8 + b = 10
b = 10 - 8
b = 2
Put the value of a and b for original number, we will get
10a + b = 10 x 8 + 2 = 80 + 2 = 82

Let us assume the present age of father = F year and Son's present age = S years
According to question, 5 years ago,
Father's age = F - 5 and Son's age = S - 5.
According to the question,
The age of the father 5 years ago was 5 times the age of his son.
F - 5 = 5(S - 5)
F - 5 = 5S - 25.....................(1)
At present the father's age is 3 times that of his son.
F = 3S.................................(2)
Put the value of F from equation (2) in equation (1), we will get
? 3S - 5 = 5S - 25
? 25 - 5 = 5S - 3S
? 20 = 2S
? 10 = S
? S = 10.
Put the value of S in Equation (2). we will get,
F = 3S = 3 x 10 = 30
So the present Age of Father = 30.

Let the ten's digit be x. Then, number = 10x + 3 and sum of digits = ( x + 3 )
So ,(x+3) = 1/7(10x + 3)
? 7x + 21 = 10x + 3
? 3x = 18
? x=6
Hence, the number = 10x + 3 = (10 x 6) + 3 = 63.

Let the number be N.
According to question,
A number is doubled and 9 is added then 2N + 9
Again According to question,
If the resultant is tripled, it becomes 75.
3 ( 2N + 9 ) = 75
? 2N + 9 = 25
?2N =16
? N = 8

Let us assume the original fraction be x/y.
According to question,
200x/100 / 200y/100 = 14/5
2x/2y = 14/5
?x/y = 14/5

Let the number be 10x + y where x > y
According to the question.
x + y = 15 ............(1)
and x - y = 3 .........(2)
Add the Equation (1) and (2) , We will get
x + y + x - y = 15 + 3
? 2x = 18
? x = 9
Put the value of x in equation (1). We will get
9 + y = 15
? y = 15 - 9
? y = 6
So we have digits of number x = 9, y = 6
? x * y = 9 * 6 = 54

According to question,
40 notebooks at the rate of ? 18 per notebook and 55 pencils at the rate of ? 8 per pencil.
Amount paid = ? (40 x 18 + 55 x 8)
Amount paid = ? (720 + 440)
Amount paid = ? 1160