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

Rohan’s age 4 years ago = 5x – 4

Rahul’s age after 4 years = 3x + 4

[latex]\frac {(5x – 4)}{(3x + 4)} = \frac {1}{1}[/latex]

Solving, we get x = 4

Rohan’s age : (5x + 4)

Rahul’s age: (3x – 4)

Ratio of Rahul’s age and Rohan’s age

[latex]\frac {(5x + 4)}{(3x - 4)} = \frac {24}{8} = \frac {3}{1} = 3:1[/latex]

Relation | Past Age (5 Yrs Ago) | Present Age | Future Age (After 6 Yrs) |
---|---|---|---|

Brother | (x – 5) | x | (x + 6) = ? |

Sister | (34 – x) - 5 | (30 – x) |

We are given, 5 years ago sister’s age was 5 times the age of her brother.

Therefore,

(34 – x) – 5 = 5 (x – 5)

34 – x – 5 = 5x – 25

5x + x = 34 – 5 + 25

6x = 54

x = 9

Future age (after 6 yrs) = (x + 6) = (9 + 6) = 15 years

Father’s age is 3 times more aged than his daughter, therefore father’s present age = x + 3x = 4x

After 5 years, father’s age is 3 times more than his daughter age.

(4x + 5) = 3 (x + 5)

x = 10

After 5 years it was (4x + 5), then after further 5 years, father’s age = (4x +10) and daughter’s age = (x + 10)

[latex]\frac {(4x + 10)}{(x + 10)} = ?[/latex]

Substitute the value of x, we get

[latex]\frac {(4x + 10) + 10}{(10 + 10)} = \frac {50}{20} = 2.5[/latex]

After further 5 years, father will be 2.5 times of daughter’s age.

G + 20 - 8 = G + 12 Years old

[latex](G - 8) \times 2 = G + 12 \rightarrow G = 28 . 28 + 10 = 38 years[/latex]

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