Question

15. The sum of ages of A and B is 85 years. 5 years ago, the age of A was twice that of B.
find the present ages.

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Answer 1

Basic Concept used :-

Writing System of Linear Equations 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.

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

$\begin{gathered}\begin{gathered}\bf\: Let-\begin{cases} &\sf{present \: age \: of \: A = x \: years} \\ &\sf{present \: age \: of \: B = y \: years} \end{cases}\end{gathered}\end{gathered}$

According to statement

Sum of ages of A and B is 85 years.

$\rm :\longmapsto\:x + y = 85 - - - (1)$

Now,

5 years ago,

$\begin{gathered}\begin{gathered}\bf\: The-\begin{cases} &\sf{ \: age \: of \: A = x - 5\: years} \\ &\sf{\: age \: of \: B = y - 5\: years} \end{cases}\end{gathered}\end{gathered}$

According to statement

Age of A is twice that of B

$\rm :\longmapsto\:x - 5 = 2(y - 5)$

$\rm :\longmapsto\:x - 5 = 2y - 10$

$\rm :\longmapsto\:x - 2y= - \: 5 - - - (2)$

On Subtracting equation (2) from equation (1), we get

$\rm :\longmapsto\:3y = 90$

$\rm :\implies\:\boxed{\bf\: y = 30}$

On substituting y = 30 in equation (1), we get

$\rm :\longmapsto\:x + 30 = 85$

$\rm :\implies\:\boxed{\bf\: x = 55}$