Question

6 years ago mothers age was 18 years more than the sons age.if the sum of their present age is 30.what was the age of mother 6 years back​

Answer 1

$\sf{\underline{\boxed{\large{\blue{\mathsf{Solution}}}}}}$

$\sf{\bold{\green{\underline{\underline{Given}}}}}$

• 6 years ago mothers age was 18 years more than the sons age
• sum of their present age is 30

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$\sf{\bold{\green{\underline{\underline{To\:Find}}}}}$

• age of mother 6 years back = ??

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$\sf{\bold{\green{\underline{\underline{Solution}}}}}$

let mother's present age be x

and son's age be y

• sum of their present age is 30 .

x + y = 30 ----- ( i )

• 6 years ago mothers age was 18 years more than the sons age

6 years ago :-

mother's age = x - 6

son's age = y - 6

x - 6 = y - 6 + 18

x - y = 6 - 6 + 18

x - y = 18 ---- ( ii )

• adding eq i and ii

$\sf\implies x + y + x - y = 30+ 18$

$\sf\implies x + x = 48$

$\sf\implies 2x = 48$

$\sf\implies x = \dfrac{48}{2}$

$\sf\implies x = 24$

Therefore :-

current age of mother = 24 years

age of mother 6 years back = 24 - 6 = 18 years

______________________

$\sf{\bold{\green{\underline{\underline{Answer}}}}}$

• 6 years back mother was 18 years old .

Answer 2

Answer:

18 years.

Step-by-step explanation:

According to Linear Equation in two variables;

Let son's present age be "x".

Let mother's present age by "y".

According to condition one(6 years ago):

(x-6) = 18+(y-6)

=> x-6 = 18+y-6

x-6 = 12+y

x= 12+y+6

x= 18+y - (i)

According to condition two (sum of their present ages):

x+y= 30

x= 30-y - (ii)

From above two equations, we get,

x = x

18+y = 30-y

2y = 12

y = 6

Put y = 6 in (ii)

x = 24

Hence, mother's present age is 24 and her son is 6 years old.

So, 6 years ago mother's age will be 18 years.

( I know this question is a little bit tricky and a little difficult to understand. You might think this method wrong but this is the correct method)

Hope you understand and best of luck for your upcoming exams✌️