Question

The mother is six times older than her son, after 4 years she will be two times as old as her son. What are their present ages?​

Answer 1

Answer:

• Mother's age = 6 years.
• Son's age = 1 year.

Given:

• The mother is six times older than her son.
• After 4 years she will be two times as old as her son.

To find:

• What are their present ages? ( mother and her son )

Step by step explanation:

Let us assume current age of mom be M

And,

Let us assume current age of son be S

$: \implies \sf M = 6S$

$: \implies \sf M + 4 = 2 (S + 4)$

$: \implies \sf M + 4 = 2 S + 8$

• As we know, M = 6S..
• So, Write M as 6S.

$: \implies \sf 6S + 4 = 2 S + 8$

$: \implies \sf 6S - 2 S=8 - 4$

$: \implies \sf 4S = 4$

$: \implies \sf S = 1$

Hence, Current age of son is 1 year.

$: \implies \sf M = 6(1)$

• Because mother's age if 6 times older then her son.

$: \implies \sf M = 6$

Hence, Mother's age is 6 years.

Answer 2

Correct Question-:

• The mother is six times older than her son, after 4 years she will be two times as old as her son. What are their present ages?

AnswEr-:

• $\underline{\boxed{\star{\sf{\blue{ The \: present \:\: of\: her\:mother \:is\: 6 \: and\: her\:son \: is \: 1 \:. }}}}}$

EXPLANATION-:

$\frak{Given \:\: -:} \begin{cases} \sf{The \:mother\: is \:six\: times\: older\: than \:her \:son.} & \\\\ \sf{After\: 4 \:years\: she \:will\: be\: two\: times \:as \:old\: as \:her \:son.}\end{cases}$

$\frak{To\:Find\: -:} \begin{cases} \sf{The \:present \: age \:of\: mother\: \: and \:her \:son.} \end{cases}$

Solution-:

• Let the present age of her mother be x .
• And ,
• The present age of her son be y .

Now ,

• $\frak{According \:To\:The\:question -:} \begin{cases} \sf{The \:mother\: is \:six\: times\: older\: than \:her \:son .} &\\\\ \sf{Then,} & \\\\ \sf{ X = 6y } \end{cases}$
• $\underline{\boxed{\star{\sf{\blue{ x = 6y }}}}}$

After 4 years -:

• $\frak{After\:4\:years\:-:} \begin{cases} \sf{Age\:of\:Son -: y + 4.\: Age \:of\:mother\:=x+4 .} &\\\\ \sf{Then,} & \\\\ \sf{After\: 4 \:years\: she \:will\: be\: two\: times \:as \:old\: as \:her \:son. } & \\\\ \sf{ Then,} & \\\\ \sf{x +4= 2(y+4) \:\:\:\:\:\: [1] } \end{cases}$

Now ,

• Equation 1 = x + 4 = 2(y +4)
• As, we know that ,
• x = 6y

Now ,

• Putting value x =6y in Equation 1 ,

Here ,

• Equation 1 = x + 4 = 2(y +4)
• x = 6y

Then ,

• $\implies{\sf{\large {6y +4 = 2(y+4)}}}$
• $\implies{\sf{\large {6y +4 = 2y+8}}}$
• $\implies{\sf{\large {6y - 2y = 8-4}}}$
• $\implies{\sf{\large {4y = 4}}}$
• $\implies{\sf{\large {y = \frac{4}{4}}}}$
• $\implies{\sf{\large {y = 1}}}$

Now ,

• $\underline{\boxed{\star{\sf{\blue{ y = 1 }}}}}$

As ,we know that ,

• $\underline{\boxed{\star{\sf{\blue{ x = 6y }}}}}$
• Here ,
• y = 1

Now ,

• x = 6(1)
• x = 6

Therefore,

• $\underline{\boxed{\star{\sf{\blue{ x = 6 }}}}}$

Therefore,

• The present of her mother = x = 6
• The present age of her son = y = 1

Hence ,

• $\underline{\boxed{\star{\sf{\blue{ The \: present \:\: of\: her\:mother \:is\: 6 \: and\: her\:son \: is \: 1 \:. }}}}}$

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