NCERT Class X Chapter 3: Pair of Linear Equations In Two Variables Exercise 3.3 Question 2(iv)

NCERT Class X Chapter 3: Pair of Linear Equations In Two Variables Exercise 3.3 Question 2(iv)

Question:

Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method:

Meena went to a bank to withdraw Rs 2000. She asked the cashier to give her Rs 50 and Rs 100 notes only. Meena got 25 notes in all. Find how many notes of Rs 50 and Rs 100 she received.

Given:

Total amount withdrawn = Rs 2000
Total number of notes = 25
Notes are of Rs 50 and Rs 100 only.

To Find:

Number of Rs 50 notes and number of Rs 100 notes.

Formula:

Let x be the number of Rs 50 notes and y be the number of Rs 100 notes.

Solution:

Forming the equations:

x + y = 25 (Total number of notes)

50x + 100y = 2000 (Total amount)

Solving by elimination method:

Multiply the first equation by 50:

50x + 50y = 1250

Subtract this from the second equation:

(50x + 100y) - (50x + 50y) = 2000 - 1250

⇒ 50y = 750

⇒ y = 750 50 = 15

Substitute y = 15 in x + y = 25:

x + 15 = 25

⇒ x = 25 - 15 = 10

Result:

Number of Rs 50 notes = 10
Number of Rs 100 notes = 15

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