A person has Rs. 5,350 in the form of denomination of Rs. 50, Rs. 100 and Rs. 500 and the total number of notes with him is 32. Find how many notes of Rs. 50, Rs.100 and Rs. 500 denominations, respectively, he has with him?

Calculation:

Let x, y, and z be the number of Rs. 50, Rs. 100, and Rs. 500 notes, respectively.

According to the question,

 x + y + z = 32 and 50x + 100y + 500z = 5350.

First, let's eliminate z from the second equation by substituting z = 32 - x - y

⇒ 50x + 100y + 500(32 - x - y) = 5350

Simplify the equation:

50x + 100y + 16000 - 500x - 500y = 5350

⇒ -450x - 400y = -10650 (Divide by -50)

9x + 8y = 213

Now, we can find a solution by trial method:

x = 13, y = 12 → 9(13) + 8(12) = 213 (This solution works)

So, x = 13 and y = 12. Now, we can find z:

z = 32 - x - y = 32 - 13 - 12 = 7

∴ The correct answer is x=13 (Rs. 50 notes), y=12 (Rs. 100 notes), and z=7 (Rs. 500 notes).