Two candles of the same length are lighted at the same time. The first is consumed in 6 hours and the second in 4 hours. Assuming that each candle burns at a constant rate, in how many hours after being lighted was the first candle twice the length of the second?
Explanation:
Let the length of each of the candles be 1 unit.
Let the first candle be twice the length of second candle after x hours of burning.
Amount of candle 1 burnt in x hours = x/6 Amount of candle 2 burnt in x hours = x/4
After x hours of burning, length remaining of Candle 1: (1 – x/6) Candle 2: (1 – x/4)
∴ (1 – x/6) = 2 × (1 – x/4)
⇒ 1 – x/6 = 2 – x/2
⇒ x = 3
∴ After 3 hours the first candle is twice the length of second.
Hence, option (a).
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