Three people A, B, and C start their journey from point X to point Y at 9:30 am, 11:30 am, and 2:00 pm respectively. The speed of B is $\sqrt{625}$ m/sec, and B reaches the destination at 7:30 pm on the same day. The speed of A is 25\% less than the speed of B. Given that B is the fastest and C is not the slowest, answer the following:

Which of the following statements are correct?

(A) A takes 2 hours 40 minutes more than B to reach the destination.

(B) A reaches the destination at 8:10 pm.

(C) The total time taken by A and B to reach the destination is 19 hours 40 minutes.

Question

Three people A, B, and C start their journey from point X to point Y at 9:30 am, 11:30 am, and 2:00 pm respectively. The speed of B is $\sqrt{625}$ m/sec, and B reaches the destination at 7:30 pm on the same day. The speed of A is 25\% less than the speed of B. Given that B is the fastest and C is not the slowest, answer the following:

Which of the following statements are correct?

(A) A takes 2 hours 40 minutes more than B to reach the destination.

(B) A reaches the destination at 8:10 pm.

(C) The total time taken by A and B to reach the destination is 19 hours 40 minutes.

Accepted Answer

**Solution:**

1. Given speed of B is $\sqrt{625} = 25$ m/sec.

2. Convert B's speed to km/hr:
   $$25 	imes \frac{18}{5} = 90 	ext{ km/hr}$$

3. B starts at 11:30 am and reaches at 7:30 pm, so total time taken by B:
   $$7:30 	ext{ pm} - 11:30 	ext{ am} = 8 	ext{ hours}$$

4. Calculate the distance between X and Y:
   $$	ext{Distance} = 	ext{Speed} 	imes 	ext{Time} = 90 	imes 8 = 720 	ext{ km}$$

5. Speed of A is 25\% less than B, so:
   $$	ext{Speed of A} = 90 	imes \left(1 - \frac{25}{100}ight) = 90 	imes \frac{3}{4} = 67.5 	ext{ km/hr}$$

6. Time taken by A to cover 720 km:
   $$\frac{720}{67.5} = 10.6667 	ext{ hours} = 10 	ext{ hours } 40 	ext{ minutes}$$

7. Difference in time between A and B:
   $$10 	ext{ hours } 40 	ext{ minutes} - 8 	ext{ hours} = 2 	ext{ hours } 40 	ext{ minutes}$$

8. A starts at 9:30 am, so A's arrival time:
   $$9:30 	ext{ am} + 10 	ext{ hours } 40 	ext{ minutes} = 8:10 	ext{ pm}$$

9. Total time taken by A and B combined:
   $$10 	ext{ hours } 40 	ext{ minutes} + 8 	ext{ hours} = 18 	ext{ hours } 40 	ext{ minutes}$$

**Note:** The total time in option (C) is given as 19 hours 40 minutes, which is incorrect.

**Answer:** (a) Both (A) & (B)

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