Question

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

Answer 1

Given:-

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

To find:-

• Their present ages.

Assumption:-

Let the present age of Reena be x

Age of Reen's mother = 4x

Solution:-

As:-

Present age of Reena is x

and present age of Reena's mother is 4x

Hence,

After 5 years,

Age of Reena = (x + 5) years

Age of Reena's mother = (4x + 5) years

Now,

According to the question,

After 5 years age of Reena's mother will be three times the age of Reena then.

Therefore,

4x + 5 = 3(x + 5)

=> 4x + 5 = 3x + 15

=> 4x - 3x = 15 - 5

=> x = 10

Now,

The present ages are as follows:-

Present age of Reena = x = 10 years

Present age of Reena's mother = 4x = 4 × 10 = 40 years.

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Verification:-

Let us see whether after 5 years age of Reena's mother comes thrice the age of Reena or not.

As the present ages of Reena and her mother are 10 years and 40 years respectively

Hence,

After 5 years

Age of Reena = 10 + 5 = 15 years

Age of Reena's mother = 40 + 5 = 45

Hence, we can see the age of Reena's mother after 5 years is thrice the age of Reena.

So the answer we got is correct.

Hence Verified!

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