Question

Deepak’s present age is one-third his mother’s present age. If the mother’s age was five times
his age 6 years ago, what are Mom & Son’s present ages?​

Answer 1

Answer:

• The ages of deepak and his mother are 12 and 36 years respectively

Step-by-step explanation:

Given:

• Deepak’s present age is one-third his mother’s present age
• His mother’s age was five times his age 6 years ago

To Find:

• what are Mom & Son’s present ages?​

Assumptions:

• Let the age of deepak's mother be x
• Let the age of deepak be 1/3 x

Accordingly:

• The age of his mother 6 years ago  = x - 6
• The agee of deepak 6 years ago = 1/3 x - 6

According to the question:

$\longrightarrow \tt 5 \bigg( \dfrac{1}{3} x - 6 \bigg) = x - 6$

$\longrightarrow \tt 5\bigg( \dfrac{x}{3} - 6\bigg ) = x - 6$

$\longrightarrow \tt \dfrac{5x}{3} - 30 = x - 6$

$\longrightarrow \tt \dfrac{5x}{3} = x - 6 + 30$

$\longrightarrow \tt \dfrac{5x}{3} - x = 24$

$\longrightarrow \tt \dfrac{5x - 3x}{3} = 24$

$\longrightarrow \tt \dfrac{2x}{3} = 24$

$\longrightarrow \tt x = \dfrac{\cancel{24}\times 3}{\cancel2}$

$\longrightarrow \tt {\purple{\underline{\boxed{\pmb{\frak{ x = 36 }}}}\bigstar}}$

The present ages are such that:

$\nrightarrow \sf Deepak's \; mother's \; age = x = 36 years$

$\nrightarrow \sf Deepak's \; age = \dfrac{x}{3} = \dfrac{36}{3} = 12 years$

Therefore:

• The ages of deepak and his mother are 12 and 36 years respectively

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Answer 2

Let the Deepak's present age = x

Let the Mother's present age = y

ATQ, x =

${\tt {\frac{1}{3} y \rightarrow y = 3x}} \: \: \: \: \: ....(1)$

6 years ago, Deepak's age = x - 6

ㅤㅤㅤㅤㅤㅤ Mother's age = y - 6

ATQ, y -6 = 5(x-6)

$\implies$ y - 6 = 5x - 30

$\implies$ y = 5x - 24 ....(1)

$\implies$ 3x = 5x - 24

$\implies$ 2x = 24

ㅤㅤㅤx = 12 = Deepak's age

ㅤㅤㅤ Mother's age = y = 3x

$\implies$ 3 × 12 = 36