# Ex.3.7 Q1 Pair of Linear Equations in Two Variables Solution - NCERT Maths Class 10

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## Question

The ages of two friends Ani and Biju differ by $$3$$ years. Ani’s father Dharam is twice as old as Ani and Biju is twice as old as his sister Cathy. The ages of Cathy and Dharam differs by $$30$$ years. Find the ages of Ani and Biju.

Video Solution
Pair Of Linear Equations In Two Variables
Ex 3.7 | Question 1

## Text Solution

Reasoning:

The difference between the ages of Biju and Ani is $$3$$ years. Either Biju is $$3$$ years older than Ani or Ani is $$3$$ years older than Biju. However, it is obvious that in both cases, Ani’s father’s age will be $$30$$ years more than that of Cathy’s age.

Steps:

Let the age of Ani and Biju be $$x$$ and $$y$$ years respectively.

Therefore, age of Ani’s father, Dharam be $$2x$$ years

And age of Biju’s sister Cathy be \begin{align}\frac{y}{2}\end{align} years

Case (I) When Ani is older than Biju

The ages of Ani and Biju differ by $$3$$ years,

$x - y = 3 \qquad \left( 1 \right)$

The ages of Cathy and Dharam differs by $$30$$ years,

\begin{align}2x - \frac{y}{2} &= 30\\4x - y &= 60 \qquad \left( 2 \right)\end{align}

Subtracting $$(1)$$ from $$(2),$$ we obtain

\begin{align}3x &= 57\\x &= 19\end{align}

Substituting $$x = 19$$ in equation $$(1),$$ we obtain

\begin{align}19 - y &= 3\\y& = 16\end{align}

Therefore, Ani is $$19$$ years old and Biju is $$16$$ years old

Case (II) When Biju is older than Ani.

The ages of Ani and Biju differ by $$3$$ years,

\begin{align}y - x &= 3\\ - x + y &= 3 \qquad \left( 1 \right)\end{align}

The ages of Cathy and Dharam differs by $$30$$ years,

\begin{align}2x - \frac{y}{2} &= 30\\4x - y &= 60 \qquad (2)\end{align}

Adding $$(1)$$ and $$(2),$$ we obtain

\begin{align}3x &= 63\\x &= 21\end{align}

Substituting $$x = 21$$ in equation $$(1),$$ we obtain

\begin{align} - 21 + y &= 3\\y &= 24\end{align}

Therefore, Ani is $$21$$ years old and Biju is $$24$$ years old.

Hence, Ani is $$19$$ years old and Biju is $$16$$ years old or Ani is $$21$$ years old and Biju is $$24$$ years old.

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