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

So as per question, 4x + 5 = 3(x + 5). So x = 10.

Hence present age of daughter is 10 years and present age of father is 40 years.

So after 5 + 5 = 10 years, daughter age would be 20 years and father’s age would be 50 years.

Hence father would be [latex]\frac {50}{20}[/latex] = 2.5 times of daughter’s age.

Aman's age before 10 years = (x - 10)

Aman's age after 20 years = (x + 20)

We are given that, Aman's age after 20 years (x + 20) is 10 times his age 10 years back (x – 10)

Therefore, (x + 20) = 10 (x – 10)

Solving the equation, we get x + 20 = 10x – 100

9x = 120, x = 13.3 years

Nisha is 15 years elder than Romi = (y + 15). So Nisha's age 5 years ago = (y + 15 – 5).

Romi's age before 5 years = (y – 5)

5 years ago, Nisha is 3 times as old as Romi

(y + 15 – 5) = 3 (y – 5)

(y + 10) = (3y – 15)

2y = 25 ⇒ y = 12.5

Romi's age = 12.5 years

Nisha's age = (y + 15) = (12.5 + 15) = 27.5 years.

Honey’s age = 2x and Piyush’s age = 3x

One year ago, their age was 2x and 3x.

Hence at present, Honey's age = 2x +1 and Piyush's age = 3x +1

After 5 years, Honey’s age = (2x +1) + 5 = (2x + 6)

Piyush's age = (3x +1) + 5 = (3x + 6)

After 5 years, this ratio becomes 4: 5. Therefore,

[latex]\frac{(2x+6)}{(3x+6)} = \frac {4}{5}[/latex]

10x + 30 = 12x + 24 [latex]\Rightarrow[/latex] x = 3

Piyush's present age = (3x + 1) = (3x 3 + 1) = 10 years

Honey's present age = (2x + 1) = (2x 3 + 1) = 7 years

At present: Mother's age is (3x + 10) and son’s age is (x + 10)

After ten years: Mother's age will be (3x + 10) +10 and son’s age will be (x + 10) + 10. Given that, mother’s age is twice that of son after ten years.

(3x + 10) + 10 = 2 [(x + 10) + 10]

(3x + 20) = 2[x + 20]

Solving the equation, we get x = 20

(3x + 10) : (x + 10) = 70 : 30 = 7 : 3.

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