Given information:
- Ratio of number of `5 coins and `10 coins is 8:15
- Value of `5 coins is `360

To find: Number of `10 coins

Solution:
1. Let's assume the number of `5 coins to be 8x and number of `10 coins to be 15x (since the ratio is given as 8:15)
2. Total value of `5 coins = `360
3. Therefore, one `5 coin has a value of `360/(8x) = `45/x
4. Total value of `10 coins = 15x * 10 = `150x
5. Now, we can equate the total value of `5 coins and `10 coins and solve for x
6. `360 = (45/x) * 8x + `150x
7. Simplifying the above equation, we get:
- 360 = 360 + 150x
- 150x = 0
- x = 0 (This is not possible)
8. Therefore, there is an error in the assumptions we made in step 1
9. Let's try assuming the number of `5 coins to be 15x and number of `10 coins to be 8x (since the ratio is given as 15:8)
10. Total value of `5 coins = 15x * 5 = `75x
11. Therefore, one `5 coin has a value of `75x/(15x) = `5
12. Total value of `10 coins = 8x * 10 = `80x
13. Now, we can equate the total value of `5 coins and `10 coins and solve for x
14. `360 = 5 * 15x + 10 * 8x
15. Simplifying the above equation, we get:
- 360 = 75x + 80x
- 155x = 360
- x = 360/155
16. Therefore, the number of `10 coins = 8x = 8 * (360/155) = 18.45 (approx)
17. Since we cannot have fractional coins, the nearest whole number to 18.45 is 18
18. Therefore, the number of `10 coins is 18

Answer: The number of `10 coins is (c) 135.

(d)135