Question

The sum of ages of a man and his son is 50 years, 5years ago , the man's age was 7 times the age of his son.
What is the present age of man ?​

Answer 1

Answer:

hello..

ig pe h ??

agar h to aja..

waha baat kar sakte h..

:)

Answer 2

$\large\underline{\sf{Solution-}}$

$\begin{gathered}\begin{gathered}\bf\: Let-\begin{cases} &\sf{present \: age \: of \: man \: be \: x \: years} \\ &\sf{present \: age \: of \: son \: be \: y \: years} \end{cases}\end{gathered}\end{gathered}$

According to statement,

☆ Sum of ages of man and son is 50 years.

$\bf\implies \:x + y = 50 - - - (1)$

5 years ago,

$\begin{gathered}\begin{gathered}\bf\: Age \: of \: -\begin{cases} &\sf{man \: be \: (x - 5) \: years} \\ &\sf{son \: be \: (y - 5) \: years} \end{cases}\end{gathered}\end{gathered}$

According to statement,

☆ Age of man be 7 times the age of son.

$\rm :\longmapsto\:x - 5 = 7(y - 5)$

$\rm :\longmapsto\:x - 5 = 7y - 35$

$\rm :\longmapsto\:x - 7y = - 30 - - - (2)$

☆ On Subtracting equation (2) from equation (1), we have

$\rm :\longmapsto\:8y = 80$

$\bf\implies \:y = 10$

☆ On substituting the value of y, in equation (1), we get

$\rm :\longmapsto\:x + 10 = 50$

$\rm :\longmapsto\:x= 50 - 10$

$\bf\implies \:x = 35$

$\begin{gathered}\begin{gathered}\bf\: Hence-\begin{cases} &\sf{present \: age \: of \: man \: be \: 40 \: years} \\ &\sf{present \: age \: of \: son \: be \: 10 \: years} \end{cases}\end{gathered}\end{gathered}$

Basic Concept Used :-

Writing System of Linear Equation from Word Problem.

1. Understand the problem.

• Understand all the words used in stating the problem.

• Understand what you are asked to find.

2. Translate the problem to an equation.

• Assign a variable (or variables) to represent the unknown.

• Clearly state what the variable represents.

3. Carry out the plan and solve the problem.