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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.
Solution :
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- Total amount withdrawn by Meena = ₹ 2000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.
More Questions from Class 10 Mathematics Pair of linear equations in two variable EXERCISE 3.3
- Q1(i): Solve the following pair of linear equations by the elimination method and the substitution method : (i) x + y = 5 and 2x – 3y = 4
- Q1(ii): Solve the following pair of linear equations by the elimination method and the substitution method : (ii) 3x + 4y = 10 and 2x – 2y = 2
- Q1(iii): Solve the following pair of linear equations by the elimination method and the substitution method : (iii) 3x – 5y – 4 = 0 and 9x = 2y + 7
- Q1(iv): Solve the following pair of linear equations by the elimination method and the substitution method : (iv) $\frac{x}{2} + \frac{2y}{3} = -1$ and $x - \frac{y}{3} = 3$
- Q2(i): Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method : (i) If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomes $\frac{1}{2}$ if we only add 1 to the denominator. What is the fraction?
- Q2(ii): Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method : (ii) Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu?
- Q2(iii): Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method : (iii) The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.
- Q2(v): Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method : (v) A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid ` 27 for a book kept for seven days, while Susy paid ` 21 for the book she kept for five days. Find the fixed charge and the charge for each extra day.
CBSE Solutions for Class 10 Mathematics Pair of linear equations in two variable
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