Question

A lady is 5 years younger to her husband and the husband is 5 times as old as his daughter. If the daughter was 5 years old 3 years back, what shall be the present age of the lady?

Answer 1

The present age of the lady shall be 35 years old.

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Let's understand a few concepts:

Let's say "x" years be the present age of a person.

We have "n" no. of years.

So,

The person's age after n years will be = (x + n) years

and

The person's age n years ago / n years back was = (x - n) years

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Let's solve the given problem:

Let's say,

"L" years → be the Lady's present age

"H" years → be the Husband's present age

"D" years → be the Daughter's present age

A lady is 5 years younger than her husband, so we can form an equation as,

$L = H - 5 \:.\:.\:.\:(1)$

The husband is 5 times as old as his daughter, so we can form the equation as,

$H = 5\times D \:.\:.\:.\:(2)$

3 years back, Daughter's age was = (D - 3) years

The daughter was 5 years old 3 years back, so we can form the equation as,

$D - 3 = 5$

$\implies D = 5 + 3$

$\implies D = 8\:years$

On substituting S = 8 years in equation (2), we get

$H = 5\times 8$

$\implies H =40\:years$

On substituting H = 40 years in equation (1), we get

$L = 40 - 5$

$\implies \bold{L = 35 \:years}$

Thus, the present age of the lady shall be 35 years.

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Answer 2

Given:

A lady is 5 years younger to her husband

and the husband is 5 times as old as his daughter.

If the daughter was 5 years old 3 years back.

to Find:

what shall be the present age of the lady.

solution:

let the present age of lady be l.

let the present age of husband be h.

let the present age of daughter be d.

as  lady is 5 years younger to her husband

∴ l = h - 5

the husband is 5 times as old as his daughter.

∴ h =5d

daughter was 5 years old 3 years back.

∴ d- 3 = 5

d = 8

∴ h = 5x8

     = 40

l = h-5

 =40 - 5

 =35

Hence the age of the lady is 35 years.