To answer this question, let's go through each option to understand why it is correct or incorrect:
Option A) 7 hours - This option is incorrect because it does not match the given information. The thicker candle lasts for 6 hours, so Ramesh could not have gone to bed 7 hours ago.
Option B) 3 hours - This option is correct. Let's see why. The thicker candle lasts for 6 hours, and the thinner candle lasts for 2 hours less than the thicker one. Therefore, the thinner candle lasts for 6 - 2 = 4 hours.
When Ramesh went to bed, he saw that the thicker candle was twice the length of the thinner one. Let's assume the length of the thinner candle is x. According to the given information, the length of the thicker candle is 2x.
Since the thicker candle lasts for 6 hours and the thinner candle lasts for 4 hours, the ratio of their lengths to their burn time is the same. Therefore, we can set up the following equation:
$\frac{2x}{6} = \frac{x}{4}$.
Simplifying this equation, we get:
$8x = 6x$.
$2x = 0$.
This implies that the length of the thinner candle is 0, which is not possible. Therefore, the assumption that the length of the thinner candle is x is incorrect.
However, we know that the length of the thinner candle is 2 hours less than the length of the thicker candle. So, if we assume the length of the thinner candle is x - 2, we can set up the following equation:
$\frac{2x}{6} = \frac{x - 2}{4}$.
Simplifying this equation, we get:
$8x = 6(x - 2)$.
$8x = 6x - 12$.
$2x = -12$.
This implies that the length of the thinner candle is -6, which is also not possible. Therefore, the assumption that the length of the thinner candle is x - 2 is incorrect.
Since both assumptions lead to contradictions, we can conclude that Ramesh did not light the candles 7 hours ago.
Option C) 4 hours - This option is incorrect because it does not match the given information. The thicker candle lasts for 6 hours, so Ramesh could not have gone to bed 4 hours ago.
Option D) 2 hours - This option is incorrect because it does not match the given information. The thicker candle lasts for 6 hours, so Ramesh could not have gone to bed 2 hours ago.
The correct answer is B) 3 hours. This option is correct because the thicker candle lasts for 6 hours and the thinner candle lasts for 2 hours less than the thicker one. Therefore, Ramesh lit the candles 3 hours ago.