Question

Solve the following word problem.

To find number of notes that Anushka had, complete the following activity.

Answer 1

Suppose, Anand gives Anushka x notes of Rs. 100 and y notes of Rs. 50 each.

∴ Value of x notes of 100 rupees = ₹ 100x

And value of y notes of 50 rupees = ₹ 50y

Based on the first condition,

∴ 100x + 50y = 2500

∴ 2x + y = 50           ...(I) (Dividing each term of the equation by 50)

Based on the second condition, the amount received on interchanging the number of notes works out to Rs. 500.

∴ 50x + 100y = 2500 − 500

∴ 50x + 100y = 2000

∴ x + 2y = 40          ...(II) (Dividing each term of the equation by 50)

Adding equation (I) and equation (II),

  2x + y = 50
+ x + 2y = 40
3x + 3y = 90

∴ x + y = 30          ...(III) (Dividing each side by 3)

Subtracting equation (II) from equation (I),

  2x + y = 50
− x + 2y = 40
−    −      −     
x − y = 10        ...(IV)

Adding equation (III) and equation (IV),

    x + y = 30
+ x − y = 10
   2x = 40

∴ x = 20

Substituting x = 20 in equation (III),

∴ 20 + y = 30

∴ y = 30 − 20

∴ y = 10

The number of 100 rupee notes is 20 and the number of 50 rupee notes is 10.