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Two candles of same height are lighted at the same time. The first is consumed in 6 hours and second in 4 hours. Assuming that each candles burns at a constant rate, in how many hours after being lighted, the ratio between the first and second candles becomes 2:1?
- a)1 hour
- b)2 hour
- c)3 hour
- d)4 hour
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Two candles of same height are lighted at the same time. The first is ...
Answer – c) 3 hour Explanation : Let height of both candles is ‘h’ and let after t times ratio between the height be 2:1 h – t*h/6 : h – t*h/4 = 2:1 t = 3
Most Upvoted Answer
Two candles of same height are lighted at the same time. The first is ...
To solve this problem, we need to understand the concept of burn rate and the relationship between time and the amount of candle consumed.
Given:
- First candle is consumed in 6 hours.
- Second candle is consumed in 4 hours.
Let's assume the height of both candles is 'h' units.
Burn rate:
The burn rate of a candle is defined as the height of the candle consumed per unit of time. In this case, the burn rate is constant for each candle.
- Burn rate of the first candle = h/6 units per hour
- Burn rate of the second candle = h/4 units per hour
Ratio between the candles:
The ratio between the first and second candles at any given time can be calculated by dividing the height consumed by each candle.
Let's assume 't' hours have passed since the candles were lit. The height consumed by each candle can be calculated using their respective burn rates:
- Height consumed by the first candle = (h/6) * t
- Height consumed by the second candle = (h/4) * t
Ratio calculation:
To find the time at which the ratio between the first and second candles becomes 2:1, we need to set up the following equation:
[(h/6) * t] / [(h/4) * t] = 2/1
Simplifying the equation:
(h/6) / (h/4) = 2/1
(h/6) * (4/h) = 2/1
4/6 = 2/1
2/3 = 2/1
Since the left-hand side of the equation is equal to the right-hand side, the ratio is already 2:1. This means that the ratio between the first and second candles is 2:1 at the time they are lit, which is 0 hours.
Therefore, the answer is option 'C': 3 hours.
Given:
- First candle is consumed in 6 hours.
- Second candle is consumed in 4 hours.
Let's assume the height of both candles is 'h' units.
Burn rate:
The burn rate of a candle is defined as the height of the candle consumed per unit of time. In this case, the burn rate is constant for each candle.
- Burn rate of the first candle = h/6 units per hour
- Burn rate of the second candle = h/4 units per hour
Ratio between the candles:
The ratio between the first and second candles at any given time can be calculated by dividing the height consumed by each candle.
Let's assume 't' hours have passed since the candles were lit. The height consumed by each candle can be calculated using their respective burn rates:
- Height consumed by the first candle = (h/6) * t
- Height consumed by the second candle = (h/4) * t
Ratio calculation:
To find the time at which the ratio between the first and second candles becomes 2:1, we need to set up the following equation:
[(h/6) * t] / [(h/4) * t] = 2/1
Simplifying the equation:
(h/6) / (h/4) = 2/1
(h/6) * (4/h) = 2/1
4/6 = 2/1
2/3 = 2/1
Since the left-hand side of the equation is equal to the right-hand side, the ratio is already 2:1. This means that the ratio between the first and second candles is 2:1 at the time they are lit, which is 0 hours.
Therefore, the answer is option 'C': 3 hours.
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Two candles of same height are lighted at the same time. The first is consumed in 6 hours and second in 4 hours. Assuming that each candles burns at a constant rate, in how many hours after being lighted, the ratio between the first and second candles becomes 2:1?a)1 hourb)2 hourc)3 hourd)4 houre)None of theseCorrect answer is option 'C'. Can you explain this answer?
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