Correct option is B
Solution:
Let the original heights of the shorter and longer candles be
H₁ and
H₂, respectively.
The burning rate (height burned per hour) for each candle is:
·
Shorter candle: H₁ / 13 per hour
·
Longer candle: H₂ / 9 per hour
After
5 hours, the remaining heights of both candles are equal:
H₁ - (5 × H₁ / 13) = H₂ - (5 × H₂ / 9)
Rearrange the equation:
H₁ (1 - 5/13) = H₂ (1 - 5/9)
Multiply the terms:
H₁ (8/13) = H₂ (4/9)
Taking the ratio H₁ / H₂:
(H₁ / H₂) = (4/9) ÷ (8/13)
(H₁ / H₂) = (4/9) × (13/8)
(H₁ / H₂) = 52 / 72
(H₁ / H₂) = 13 / 18
Final Answer:
(b) 13:18.
