Question

Presently Ram's uncle is 16 years older than Ram. 8 years after his uncle age will be twice as his age. Find the present age of Ram and his uncle (With the help of graph)​

Answer 1

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

According to statement,

• Ram's uncle is 16 years older than Ram.

$\rm :\longmapsto\:y - x = 16 - - - (1)$

After 8 years,

$\begin{gathered}\begin{gathered}\bf \:Let \: age \: of \: -\begin{cases} &\sf{Ram \: be \: x + 8 \: years} \\ &\sf{Ram \: uncle \: be \: y + 8 \: years} \end{cases}\end{gathered}\end{gathered}$

According to statement,

• Ram uncle age be twice the Ram age

$\rm :\longmapsto\:y + 8 = 2(x + 8)$

$\rm :\longmapsto\:y + 8 = 2x + 16$

$\rm :\longmapsto\:y - 2x = 16 - 8$

$\rm :\longmapsto\:y - 2x = 8 - - - (2)$

Now,

we have two linear equations

$\sf \: \: \: \: \: \: \: \: \: \bull \: \: \: y - x = 16$

$\sf \: \: \: \: \: \: \: \: \: \bull \: \: \: y - 2x = 8$

Consider,

$\sf \: \: \: \: \: \: \: \: \: \bull \: \: \: y - x = 16$

1. Substituting 'x = 0' in the given equation, we get

$\rm :\longmapsto\:y - 0 = 16$

$\bf\implies \:y = 16$

2. Substituting 'y = 0' in the given equation, we get

$\rm :\longmapsto\:0 - x = 16$

$\bf\implies \:x = - \: 16$

Hᴇɴᴄᴇ,

➢ Pair of points of the given equation are shown in the below table.

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf 16 \\ \\ \sf - 16 & \sf 0 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points (0 , 16) & (- 16 , 0)

➢ See the attachment graph. (Red color line)

Now,

Consider,

$\sf \: \: \: \: \: \: \: \: \: \bull \: \: \: y - 2x = 8$

1. Substituting 'x = 0' in the given equation, we get

$\rm :\longmapsto\:y - 2 \times 0 = 8$

$\bf\implies \:y = 8$

2. Substituting 'y = 0' in the given equation, we get

$\rm :\longmapsto\:0 - 2x = 8$

$\bf\implies \:x = - 4$

Hᴇɴᴄᴇ,

➢ Pair of points of the given equation are shown in the below table.

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf 8 \\ \\ \sf - 4 & \sf 0 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points (0 , 8) & (- 4 , 0)

➢ See the attachment graph. (Purple color line)

So, From graph, we concluded that the two lines intersect at (8, 24).

$\begin{gathered}\begin{gathered}\bf \:Hence \: present \: age \: of \: -\begin{cases} &\sf{Ram \: be \: 8\: years} \\ &\sf{Ram \: uncle \: be \: 24 \: years} \end{cases}\end{gathered}\end{gathered}$