Q2(iv):

Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method : (iv) Meena went to a bank to withdraw ` 2000. She asked the cashier to give her ` 50 and ` 100 notes only. Meena got 25 notes in all. Find how many notes of ` 50 and ` 100 she received.

Given:

• Total amount withdrawn by Meena = ₹ 2000
• Types of notes received = ₹ 50 notes and ₹ 100 notes
• Total number of notes received = 25

To Find:

The number of ₹ 50 notes and the number of ₹ 100 notes received by Meena.

Step 1: Defining Variables

Let $x$ be the number of ₹ 50 notes.

Let $y$ be the number of ₹ 100 notes.

Step 2: Formulating the Equations

Based on the total number of notes:

$x + y = 25$ --- (Equation 1)

Based on the total value of the notes:

$50x + 100y = 2000$ --- (Equation 2)

To simplify Equation 2, we divide the entire equation by 50:

$\frac{50x}{50} + \frac{100y}{50} = \frac{2000}{50}$

$x + 2y = 40$ --- (Equation 3)

Step 3: Solving by Elimination Method

We have the system of equations:

(1) $x + y = 25$

(3) $x + 2y = 40$

Subtract Equation 1 from Equation 3 to eliminate the variable $x$:

$(x + 2y) - (x + y) = 40 - 25$

$x - x + 2y - y = 15$

$y = 15$

Step 4: Finding the value of $x$

Substitute the value of $y = 15$ into Equation 1:

$x + 15 = 25$

$x = 25 - 15$

$x = 10$

Step 5: Verification

Check the total number of notes: $10 + 15 = 25$ (Correct).

Check the total value: $50(10) + 100(15) = 500 + 1500 = 2000$ (Correct).

Final Answer:

Meena received 10 notes of ₹ 50 and 15 notes of ₹ 100.