Question

Rakhi's mother is four times as old as Rakhi. After 5 years, her mother will be three times as old as she will be then. Find their present ages.​

Answer 1

AnSwer :

» Let the present age of Rakhi be m years.

Given that,

• Rakhi's Mother is four times the age of Rakhi.

⇥ Rakhi's mother = 4(Rakhi's age)

⇥ Rakhi's mother = 4m years

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Also,

• After five years, her mother will be three times as old as she will be then.

Then, After five years —

• Rakhi's age = (m + 5) years
• Rakhi's mother = (4m + 5) years

⠀

☆ Mother's age = 3(Rakhi's age) ☆

➟ (4m + 5) = 3(m + 5)

➟ 4m + 5 = 3m + 15

➟ 4m – 3m = 15 – 5

➟ m = 10

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Therefore,

• Present age of Rakhi, m = 10 years
• Present age of Mother, 4m = 4(10) = 40 years

∴ Hence, Present age of Rakhi and Mother is 10 years and 40 years respectively. $\;$

Answer 2

Given :-

Rakhi's mother is four times as old as Rakhi. After 5 years, her mother will be three times as old as she will be then.

To Find :-

Find their present ages

Solution :-

Let the age of Rakhi be x and Rakhi's mother be y

4x = y (i)

After 5 years

Age of mother = 3(Age of Rakhi)

y + 5= 3(x + 5)

y + 5  = 3x + 15

Using Eq (i)

4x + 5 = 3x + 15

4x - 3x = 15 - 5

x = 10

Again, using Eq (i)

4x = y

4(10) = y

40 = y

Therefore

Age of Rakhi = x = 10 years

Age of Rakhi's mother = y = 40 years