Three people A, B, and C start their journey from point X to 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. It is known that B is the fastest and C is not the slowest. Which of the following statements is/are correct?

(A) C reached the destination in 6 hours and A reached the destination in 4.5 hours.

(B) C reached the destination in 5 hours and A reached the destination in 9 hours.

(C) If the distance is increased by 180 km and the speed of C is $\frac{1}{6}$th of the speed of B, then A reaches the new destination at 4:20 pm.

Question

Three people A, B, and C start their journey from point X to 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. It is known that B is the fastest and C is not the slowest. Which of the following statements is/are correct?

(A) C reached the destination in 6 hours and A reached the destination in 4.5 hours.

(B) C reached the destination in 5 hours and A reached the destination in 9 hours.

(C) If the distance is increased by 180 km and the speed of C is $\frac{1}{6}$th of the speed of B, then A reaches the new destination at 4:20 pm.

Accepted Answer

**Solution:**

1. **Calculate speed of B:**
   - Given speed of B = $\sqrt{625} = 25$ m/sec
   - Convert to km/hr: $25 	imes \frac{18}{5} = 90$ km/hr

2. **Calculate total distance:**
   - B starts at 11:30 am and reaches at 7:30 pm, total time = 8 hours
   - Distance = speed $	imes$ time = $90 	imes 8 = 720$ km

3. **Analyze speed order:**
   - Given B is fastest, C is not slowest, so order of speeds is $B > C > A$

4. **Check statement (A):**
   - (A) claims C took 6 hours and A took 4.5 hours
   - Since A is slowest, A should take more time than C and B
   - Here, A's time (4.5 hours) is less than C's (6 hours), which contradicts the order
   - Hence, (A) is incorrect

5. **Check statement (B):**
   - (B) claims C took 5 hours and A took 9 hours
   - Since C is slower than B, C should take more than 8 hours (B's time)
   - Here, C's time is less than B's, so (B) is incorrect

6. **Check statement (C):**
   - New distance = $720 + 180 = 900$ km
   - Speed of C = $\frac{1}{6}$ of B's speed = $\frac{1}{6} 	imes 90 = 15$ km/hr
   - Time taken by C = $\frac{900}{15} = 60$ hours
   - Since A is slower than C, A takes more than 60 hours
   - So A cannot reach at 4:20 pm (which is just a few hours after start)
   - Hence, (C) is incorrect

**Answer:** (b) None of these

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