Question

Sum of the ages of mother and son is 45 years. If son's age is subtracted from twice of mother's age then we get answer 54. Find the ages of mother and son. It becomes easy to solve a problem if we make use of variables.​

Answer 1

$\huge\underline\frak{\fbox{AnSwEr :-}}$

Let the mother's today's age be x years and son's today's age be y years.

From the first condition

$\implies$ x + y = 45 ......... (I)

From the second condition

$\implies$ 2 x - y = 54 ......... (II)

Adding equations (I) and (II)

$\implies$ 3x + 0 = 99

$\implies$ 3x = 99

$\implies$ x = 33

Substituting x = 33 in equation (I),

$\implies$ 33 + y = 45

$\implies$ y = 45 - 33

$\implies$ y = 12

Verify that x=33 and y = 12 is the solution of second equation.

$\therefore$ Today's age of mother = 33 and today's age of son = 12.

Answer 2

Solution :

$\bf{\red{\underline{\bf{Given\::}}}}$

Sum of the ages of mother and son is 45 years.If the son's age is subtracted from twice of mother's age then we get answer 54.

$\bf{\red{\underline{\bf{To\:find\::}}}}$

The age of mother and son.

$\bf{\red{\underline{\bf{Explanation\::}}}}$

Let the age of Mother's be r years

Let the age of Son's be m years

$\dag\:\underline{\underline{\bf{According\:to\:the\:question\::}}}}}$

$\longrightarrow\sf{r+m=45}\\\\\longrightarrow\sf{r=45-m.......................(1)}$

&

$\longrightarrow\sf{2r-m=54}\\\\\\\longrightarrow\sf{2(45-m)-m=54\:\:\:\:[from(1)]}\\\\\\\longrightarrow\sf{90-2m-m=54}\\\\\\\longrightarrow\sf{90-3m=54}\\\\\\\longrightarrow\sf{-3m=54-90}\\\\\\\longrightarrow\sf{-3m=-36}\\\\\\\longrightarrow\sf{m=\cancel{\dfrac{-36}{-3} }}\\\\\\\longrightarrow\sf{\pink{m=12\:years}}$

Putting the value of m in equation (1),we get;

$\longrightarrow\sf{r=45-12}\\\\\longrightarrow\sf{\pink{r=33\:years}}$

Thus;

$\dag\underbrace{\sf{The\:age\:of\:Mother\:is\:r=33\:years.}}}}}}\\\dag\underbrace{\sf{The\:age\:of\:Son's\:is\:m=12\:years.}}}}}}$