If the current age of a person be X, then

- age after n years = X + n
- age n years ago = X – n
- n times the age = nX
- If ages in the numerical are mentioned in ratio A : B, then A : B will be AX and BX

[latex](4X + 8) = \frac {5}{2} x (X + 8)[/latex]

8X + 16 = 5X + 40

3X = 24 so, X = 8

Hence, required ratio = [latex] \frac {(4X + 16)}{(X + 16)} = \frac {48}{24} = 2 [/latex]

2X = 38

X = 19

Son’s age 5 years back = (19 – 5) years = 14 years

Sam’s age be 4X years

And, Ash’s age be 3X years

Present age of Sam = (4X + 1) years

Present age of Ash= (3X + 1) years

One year hence

Sam’s age = (4X + 2) years

Ash’s age = (3X + 2) years

According to question,

[4X + 2] divide by [3X + 2] = [latex]\frac {5}{4}[/latex]

16X + 8 = 15X + 10

or, X = 2

Sum of their present ages = 4X + 1 + 3X + 1

= 7X + 2

= 7 x 2 + 2 = 16 years.

(P - 8) = 2(Q - 8)

P - 2Q = -8______(1)

P - Q = 6 ___(2)

Solve (1) & (2)

Q = 14

P - 2Q = -8______(1)

P - Q = 6 ___(2)

Solve (1) & (2)

Q = 14

E - 12 = 3(Y - 12)

E - 3Y = -24_______(2)

Solve (1)& (2)

Y = [latex]\frac {30}{2} = 15[/latex]

E = 15 + 6 = 21

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