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

Question

Accepted Answer

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

We have two equations:
1) x + y + z = 25 (total coins)
2) 10x + 5y + 2z = 120 (total value)

Let's solve these equations step by step:

From (1): z = 25 - x - y

Substitute z in (2):
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, y must be an integer, so try values of x that make y integer and all variables non-negative.

8x + 3y = 70
=> 3y = 70 - 8x
=> y = (70 - 8x)/3

Try x = 8:
y = (70 - 8*8)/3 = (70 - 64)/3 = 6/3 = 2

So, x = 8, y = 2, z = 25 - 8 - 2 = 15

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

All conditions are satisfied. So, the number of ₹10 coins used is 8.

Hence, the correct answer is option 4: 8.

Answer

Answer

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