In a palace, three different types of coins are there namely gold, silver and…
2024
In a palace, three different types of coins are there namely gold, silver and bronze. The number of gold, silver and bronze coins is 18000, 9600 and 3600 respectively.
Find the minimum number of rooms required if in each room should give the same number of coins of the same type.
- A.
12
- B.
18
- C.
26
- D.
24
Attempted by 5 students.
Show answer & explanation
Correct answer: C
To find the minimum number of rooms required, you need to ensure that the number of coins of the same type in each room is the same and maximized. This is achieved by finding the Highest Common Factor (H.C.F.) of the three types of coins.
Step-by-Step Calculation
1. Find the H.C.F. of 18000, 9600, and 3600:
To simplify, you can find the H.C.F. of 180, 96, and 36 and then multiply by 100 at the end.
180 = 12 * 15 = 2^2 * 3^2 * 5
96 = 12 * 8 = 2^5 * 3
36 = 12 * 3 = 2^2 * 3^2
The H.C.F. of 180, 96, and 36 is 12.
Multiplying by 100, the H.C.F. is 1200. This represents the maximum number of coins of one type per room.
2. Calculate the number of rooms for each type of coin:
Now, divide the total number of each coin by the H.C.F. (1200):
Rooms for gold coins: 18000 / 1200 = 15
Rooms for silver coins: 9600 / 1200 = 8
Rooms for bronze coins: 3600 / 1200 = 3
3. Find the total number of rooms:
Total rooms = 15 + 8 + 3 = 26.