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23 Dec 2025, 11:09
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At the end of every 6 hours, Hermoine’s beans are increased by 200% or multiplied by 3
At the end of every 18 hours, Ron’s beans are increased by 800% or mutiplied by 9
Let x= the number of 18 hour intervals
Thus,
27 * \(3^(3x)\) = 729 * \(9^x\)
\(3^3\) * \(3^(3x)\) = \(3^6\) * \(3^(2x)\)
Since the base is the same,
3 + 3x = 6 + 2x
x=3
Thus, no. of hours = 3*18 = 54
At the end of every 18 hours, Ron’s beans are increased by 800% or mutiplied by 9
Let x= the number of 18 hour intervals
Thus,
27 * \(3^(3x)\) = 729 * \(9^x\)
\(3^3\) * \(3^(3x)\) = \(3^6\) * \(3^(2x)\)
Since the base is the same,
3 + 3x = 6 + 2x
x=3
Thus, no. of hours = 3*18 = 54
Bunuel
23 Dec 2025, 11:12
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Answer C
at 0 hours:
Hermione (H) -> 27 beans = 3^3
Ron (R) -> 729 beans = 3^6
at the end of every 6h -> multiply H by 3
at the end of every 18h -> multiply R by 3^2
after 6h:
H = 3^4
R = 3^6
after 12h:
H = 3^5
R = 3^6
after 18h:
H = 3^6
R = 3^8
after 30h
H = 3^8
R = 3^8
at 0 hours:
Hermione (H) -> 27 beans = 3^3
Ron (R) -> 729 beans = 3^6
at the end of every 6h -> multiply H by 3
at the end of every 18h -> multiply R by 3^2
after 6h:
H = 3^4
R = 3^6
after 12h:
H = 3^5
R = 3^6
after 18h:
H = 3^6
R = 3^8
after 30h
H = 3^8
R = 3^8
23 Dec 2025, 11:30
Kudos
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We can say that there are 3^3 beans with Hermoine which increase by a factor of 3 (200% increase corresponds to 3x increase) every 6 hours. On the other hand, there were 3^5 beans with Ron which increases by a factor of 3^2 every 18 hours (3^7 beans)
Consider the next 18 hr period. In this case, the number of beans grow to 3^9
In the total 36 hr period, beans with hermoine grow by 3 for 6 periods. Therefore, 3^3 grows to 3^(6+3) or 3^9.
We can conclude that at the 36 hr period, the number of beans do match.
Therefore, Option D
Consider the next 18 hr period. In this case, the number of beans grow to 3^9
In the total 36 hr period, beans with hermoine grow by 3 for 6 periods. Therefore, 3^3 grows to 3^(6+3) or 3^9.
We can conclude that at the 36 hr period, the number of beans do match.
Therefore, Option D
