A payment of ₹120 is made with ₹10, ₹5 and ₹2 coins. A total of 25 coins are used. Which of the following is the number of ₹10 coins used in the payment?

Question

Accepted Answer

Let the number of ₹10, ₹5, and ₹2 coins be x, y, and z respectively.

We have two equations:
1) Total coins: x + y + z = 25
2) Total amount: 10x + 5y + 2z = 120

From the first equation, z = 25 - x - y.

Substitute z in the second equation:
10x + 5y + 2(25 - x - y) = 120
10x + 5y + 50 - 2x - 2y = 120
(10x - 2x) + (5y - 2y) + 50 = 120
8x + 3y + 50 = 120
8x + 3y = 70

Now, solve for y:
3y = 70 - 8x
y = (70 - 8x)/3

Since y must be a non-negative integer, (70 - 8x) must be divisible by 3 and y ≥ 0.

Check options for x:
- x = 6:
  y = (70 - 8*6)/3 = (70 - 48)/3 = 22/3 ≈ 7.33 (not integer)
- x = 4:
  y = (70 - 8*4)/3 = (70 - 32)/3 = 38/3 ≈ 12.67 (not integer)
- x = 10:
  y = (70 - 8*10)/3 = (70 - 80)/3 = -10/3 (negative, invalid)
- x = 8:
  y = (70 - 8*8)/3 = (70 - 64)/3 = 6/3 = 2 (valid)

For x = 8, y = 2, then z = 25 - 8 - 2 = 15.

Check total amount:
10*8 + 5*2 + 2*15 = 80 + 10 + 30 = 120

Thus, the number of ₹10 coins used is 8.

Rechecking the options, the correct answer is 8.

Answer

Answer

Answer