Question

Sippy brought home 2 tortoise as pets. She collected money to build a comfortable home for them. She had a total of Rs. 8200 in the form of Rs. 100, Rs. 500 and Rs. 2000 currency notes.

Rs. 500 notes were half of Rs. 100 notes. Rs. 2000 were one-third of Rs. 500 notes.
i) Write and solve the linear equation to find the number of notes of each denominations.
ii) Calculate the value of money obtained from Rs. 100 notes.

Answer 1

Let x be the number of Rs. 100 notes, y be the number of Rs. 500 notes, and z be the number of Rs. 2000 notes.

From the given information, we have the following equations:

y = 0.5x (Rs. 500 notes were half of Rs. 100 notes)
z = (1/3)y (Rs. 2000 were one-third of Rs. 500 notes)
100x + 500y + 2000z = 8200 (Total value of money)

Substituting y = 0.5x in the second equation, we get:

z = (1/3)(0.5x) = (1/6)x

Substituting y = 0.5x and z = (1/6)x in the third equation, we get:

100x + 500(0.5x) + 2000((1/6)x) = 8200

Simplifying this equation, we get:

100x + 250x + 333.33x = 8200
683.33x = 8200
x ≈ 12

Therefore, Sippy has 12 Rs. 100 notes, 6 Rs. 500 notes (y = 0.5x), and 2 Rs. 2000 notes (z = (1/6)x).

The value of money obtained from Rs. 100 notes is 100x = 100(12) = Rs. 1200