When 20 is subtracted from a number , it reduces to seven- twelve of the number. What is the sum of the digit of the number?

Let us assume the ratio factor is x.
Then the three numbers be 5x , 9x and 11x respectively.
Then according to question,
5x + 9x + 11x = 300
? 25x = 300
? x = 12
So, the second number is 9x = 9 x 12 =108

Let the middle number = x , then first number = x - 2 and last number = x + 2
(x - 2) + x + (x + 2) = 176/4 - 14
x - 2 + x + x + 2 = 44 - 14
3x = 30
x = 10
So middle number = x = 10

Let the two numbers be x and y .
According to question,
? xy = 192...................... (1)
x + y = 28........................(2)
As we know that,
(x - y)² = (x + y)² - 4xy
Put the value of xy and x + y from equation (1) and (2), we will get
(x - y)² = (28)² - 4 x 192
? (x - y)² = 784 - 786
? (x - y)² = 16
? x - y = 4......................(3)
Add the equation (2) and (3), we will get
x + y + x - y = 28 + 4
2x = 32
x = 16
Put the value of x in equation (2), we will get
16 + y = 26
y = 28 - 16
y = 12

So numbers are x = 16 and y = 12.
Smaller number is 12.

Let us assume father age is F and his son age is S.
According to question,
The sum of the ages of father and his son is 4 times the age of the son,
F + S = 4S
F = 3S.............. (1)
Average age of father and son is 28.
(F + S)/2 = 28
F + S = 56
Put the value of F from equation from (1),
3S + S = 56
4S = 56
S = 14 years
Age of Son = 14 years.

Method 1
Let us assume the number be 3p , 3(p+1) and 3(p+2)
According to question,
3p + 3(p+1) + 3(p+2) = 72
? 3p + 3p + 3 +3p + 6 = 72
? 9p +9 = 72
? 9p = 72 - 9
? 9p = 63
? p = 63/9 = 7
? Largest number = 3(p + 2)
Put the value of p in above equation.
? Largest number = 3 x ( 7 + 2 )
? Largest number = 3 x 9
? Largest number = 27

Method 2
Let us assume the numbers P , P + 3 ,P+ 6
According to Question,
sum of three numbers = 72
P + P + 3 + P + 6 = 72
? 3P + 9 = 72
? 3P = 72 - 9
? 3P = 72 - 9
? P = 63/3
? P = 21
So largest Number = P + 6 = 21 + 6 = 27

Let us assume 1 pen cost be ? x and 1 pencil cost be ? y.
According to question,
The Cost of 36 pens and 42 pencils is 460.
36x + 42y = 460 ...................(1)
then the cost of 18 pens and 21 pencils = 18x + 21y.
Now divide the Equation (1) by 2. We will get,
18x + 21y = 230
So the Cost of 18 pens and 21 pencils = 18x + 21y = 230

Cost of 5 pens + 8 pencils = ?31
On multiplying by 3
15 pens + 24 pencils = 3 x 31 =
?15 pens + 24 pencils = 93

2x + 3y = 29 ...(i)
and y = x + 3 ...(ii)
Putting the value of y from Eq. (ii) to Eq. (i), we get
2x + 3y = 29
2x + 3(x + 3) = 29
2x + 3x + 9 = 29
? 5x = 20
? x = 4

3x + 7y = 75 ..(i)
5x - 5y = 25
? x - y = 5 ...(ii)
On multiplying Eq. (ii) by 7 and adding to Eq. (i), we get
3x + 7y = 75
7x - 7y = 35
------------------
10x = 110
x = 11
? Putting the value of x in Eq. (ii), we get
11 - y = 5
? y = 6
? x + y = 6 + 11 = 17

we have, x + y - 7 = 0
? x + y = 7 ...(i)
and 3x + y - 13 = 0
? 3x + y = 13 ..(ii)
By subtracting Eq. (i) from Eq. (ii), we get
3x + y = 13
x + y = 7
----------------------
2x = 6 ...(ii)
? x = 3

On putting the value of x in Eq. (i), we get
3 + y = 7
? y = 4

Now, 4x² + y² + 4xy
= 4 x (3)² + (4)² + 4 x 3 x 4
= 4 x 9 + 16 + 48
= 36 + 16 + 48 = 100