Question

Deepak's present age is one third of his mother's present age. if the mother's age was 5 times his age 6 years ago,what are their age now

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Answer 1

Given:

• Deepak's present age is one-third of his mother present age.

• The mother age was 5 times Deepak's age before 6 years ago.

To find:

Now, we need to find the age of both mother and Deepak.

Solution:

• So, we will consider mother present age as X.

• Let, consider Deepak's present age as $\frac{x}{3}$
• 6 years ago mother age was X- 6
• Let's Deepak's present age $\frac{x}{3}$ - 6

Now, X- 6 = 5 ( $\frac{x}{3}$ - 6)  

We will solve this equation.

X - 6 = 5 $\frac{x}{3}$ - 30

Here, we will move the variables to one side.

- 6 + 30 = 5 $\frac{x}{3}$ - X    

24 = $\frac{5x - 3x}{3}$

24 = $\frac{2x}{3}$

2x = 24 × 3

2x = 72

X = $\frac{72}{2}$

X = 36  

∴Mother's age = 36 years  

Deepak's present age = $\frac{x}{3}$

                                     = $\frac{36}{3}$

Deepak's present age = 12 years

∴ Mother's present age is 36 years old

  Deepak's present age 12 years old