In covering a certain distance , the speeds of A and B are in the ratio of 3 : 4. A takes 30 minutes more than B to reach the destination. The time taken by A to reach the destination is :
এই প্রশ্নটি সহ গণিত বিষয়ের আরও কিছু গুরুত্বপূর্ণ প্রশ্ন আছে
১ + ৫ + ৯ + ........... +৮১ = ?
In covering a certain distance, the speeds of A and B are in the ratio of 3:4. A takes 30 minutes more than B to reach the destination. The time taken by A to reach the destination is:
Choices: ['1.0 hour', '1.5 hours', '2.0 hours', '2.5 hours']
Correct Answer: '2.0 hours'
<h2>Explanation:</h2>To solve this problem, we will use the relationship between speed, distance, and time. The formula for this relationship is:
$ \text{Speed} = \frac{\text{Distance}}{\text{Time}} $
Given that the speeds of A and B are in the ratio of 3:4, we can express the speeds as:
$ \text{Speed of A} = 3x $ and $ \text{Speed of B} = 4x $
Let the time taken by B to cover the distance be $ t $ hours.
Then the time taken by A, who takes 30 minutes more than B, will be:
$ t + \frac{30}{60} $ hours, which simplifies to $ t + 0.5 $ hours.
Since distance is constant for both A and B, we can write:
$ \text{Speed of A} \times \text{Time of A} = \text{Speed of B} \times \text{Time of B} $
Substitute the given speeds and times:
$ 3x \times (t + 0.5) = 4x \times t $
Divide both sides by $ x $ (assuming $ x \neq 0 $) to simplify:
$ 3(t + 0.5) = 4t $
Expand and solve for $ t $:
$ 3t + 1.5 = 4t $
Rearrange to isolate $ t $:
$ 4t - 3t = 1.5 $
$ t = 1.5 $ hours
So, the time taken by B is $ 1.5 $ hours. To find the time taken by A:
$ \text{Time taken by A} = t + 0.5 = 1.5 + 0.5 = 2.0 $ hours
Therefore, the correct answer is '2.0 hours'.
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