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CAT 2024 Slot 2 QA Question 8

Multiple choice (+3 / −1) · Arithmetic · Time, Speed & Distance · Try it, then check the answer and solution below.

CAT 2024 Slot 2QAArithmetic • Time, Speed & DistanceModerate
A bus starts at 9 am and follows a fixed route every day. One day, it traveled at a constant speed of 60 km per hour and reached its destination 3.5 hours later than its scheduled arrival time. Next day, it traveled two-thirds of its route in one-third of its total scheduled travel time, and the remaining part of the route at 40 km per hour to reach just on time. The scheduled arrival time of the bus is
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Answer and solution

Answer: C) 7:30 pm

📌 Core Concept
The problem involves calculating the scheduled arrival time of a bus using the relationship between speed, distance, and time. The key formula is:
Distance=Speed×Time\text{Distance} = \text{Speed} \times \text{Time}
🔢 Step-by-Step Solution
1
Define Variables:
Let TT be the scheduled travel time in hours.
Let DD be the total distance of the route in km.
2
First Day:
Speed = 60 km/h
Time taken = T + 3.5$ hours
Distance:
D=60×(T+3.5)D = 60 \times (T + 3.5)
3
Second Day:
First part: 23D\frac{2}{3}D at 13\frac{1}{3}T$ time.
Speed for first part:
23D13T=2DT−Secondpart:\frac{\frac{2}{3}D}{\frac{1}{3}T} = \frac{2D}{T} - Second part:13\frac{1}{3}D$ at 40 km/h.
Time for second part:
\frac{ \frac{1}{3}D}{40} = D120\frac{D}{120} - Total time: 13T+D120=T\frac{1}{3}T + \frac{D}{120} = T$
4
Substitute DD from Day 1 into Day 2 equation:
D=60(T+3.5)D = 60(T + 3.5)
Substitute:
13T+60(T+3.5)120=T13T+T+3.52=T\frac{1}{3}T + \frac{60(T + 3.5)}{120} = T \frac{1}{3}T + \frac{T + 3.5}{2} = T
5
Solve for TT:
Multiply all terms by 6:
2T+3(T+3.5)=6T2T+3T+10.5=6T5T+10.5=6TT=10.5 hours2T + 3(T + 3.5) = 6T 2T + 3T + 10.5 = 6T 5T + 10.5 = 6T T = 10.5 \text{ hours}
6
Calculate Scheduled Arrival Time:
Start time: 9 am
Add 10.5 hours: 9 am + 10 hours 30 minutes = 7:30 pm
⚡ 30-Second Shortcut
Recognize that the second day's time equation simplifies to T=10.5T = 10.5 hours.
Adding 10.5 hours to 9 am gives 7:30 pm.
🎯 Final Answer
Correct Answer: C

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