Let's analyze the information to find the number of Tk. 5 denomination notes Mr. X had:

1. Total Amount: We are given that the total amount of money in the wallet was Tk. 120.
2. Note Denominations: The notes were only in Tk. 2 and Tk. 5 denominations.
3. Total Number of Notes: There were 30 notes in total.

Since we only have Tk. 2 and Tk. 5 notes, the total amount must be a multiple of 5. This eliminates option (a) (15).

Let's denote the number of Tk. 5 notes as x and the number of Tk. 2 notes as y. We can set up two equations based on the given information:

• Equation 1 (Total Amount): 5x + 2y = 120 (The value of each Tk. 5 note is multiplied by x, and the value of each Tk. 2 note is multiplied by y, and the sum equals the total amount)
• Equation 2 (Total Number of Notes): x + y = 30 (The total number of Tk. 5 notes (x) plus the number of Tk. 2 notes (y) equals the total number of notes)

We can solve this system of equations to find x (the number of Tk. 5 notes). However, there's a shortcut:

• Notice that in equation 1, if we divide both sides by 5, we get: x + (2/5)y = 24. This equation looks very similar to equation 2, except the coefficient of y is slightly different (2/5 instead of 1).

This suggests that if we substitute a value for y in equation 1 that is a multiple of 5, the equation will be easier to solve for x. In this case, since the total number of notes (x + y) is 30, and y represents the number of Tk. 2 notes, then y must be an even number (because you cannot have half notes). Let's try substituting y = 20 (an even multiple of 5) into equation 1:

• 5x + 2(20) = 120
• 5x + 40 = 120
• 5x = 80
• x = 16

Therefore, Mr. X had 16 Tk. 5 denomination notes. This corresponds to option (c).