If Raj travels at speed of 24 km/hr, he reaches his destination 15 minutes late, however if he travels at speed of 26 km/hr, he reaches his destination 20 minutes early. Find the time taken by Raj to reach destination if he travels at speed of 13 km/hr.a)14 hrb)7 hrc)7.5 hrd)15 hrCorrect answer is option 'A'. Can you explain this answer?

Question

Answer

To solve this problem, let's assume the distance to the destination is 'd' km.

Given:
Speed 1: 24 km/hr (15 minutes late)
Speed 2: 26 km/hr (20 minutes early)

We can calculate the time taken to reach the destination at each speed using the formula:

Time = Distance / Speed

1. Time taken at Speed 1:
Time1 = d / 24 km/hr

2. Time taken at Speed 2:
Time2 = d / 26 km/hr

According to the given information, Raj reaches his destination 15 minutes late at Speed 1 and 20 minutes early at Speed 2.

3. Time taken at Speed 1 (15 minutes late):
Time1 + 15/60 = d / 24 km/hr

4. Time taken at Speed 2 (20 minutes early):
Time2 - 20/60 = d / 26 km/hr

Now, we can solve these two equations to find the value of 'd'.

Time1 + 15/60 = d / 24
Time2 - 20/60 = d / 26

Since both equations are equal to 'd', we can equate them:

d / 24 = d / 26 - (20/60 - 15/60)

Simplifying the equation:

d / 24 = d / 26 - 5/60
d / 24 - d / 26 = -5/60
(26d - 24d) / (24 * 26) = -5/60
2d / (24 * 26) = -5/60

Cross-multiplying:

(2d * 60) = (-5) * (24 * 26)
120d = -5 * (24 * 26)
120d = -5 * 624
120d = -3120
d = -3120 / 120
d = -26

Since distance cannot be negative, there seems to be an error in the question or the given information.

However, if we assume that the distance is positive, we can proceed with the calculations.

Let's calculate the time taken at a speed of 13 km/hr:

Time at Speed 3:
Time3 = d / 13 km/hr

Since we don't have the actual value of 'd', we cannot calculate the exact time taken at Speed 3. Therefore, we cannot determine the correct answer from the given options.

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