NinetynineCAT 2024 Slot 2 QA Q17 Time, Speed & Distance
Question 17 of the Quantitative Ability (QA) section, CAT 2024 Slot 2, with CAT's official answer and a worked solution.
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
- A10 : 30 pm
- B7 : 00 pm
- C7 : 30 pm
- D9 : 00 pm
Answer: (C) 7 : 30 pm Time, Speed & Distance MCQ
Solution
- Let route length \(D\) km and scheduled travel time \(T\) hours. Day 1: \(\frac{D}{60} = T + 3.5\).
- Day 2: the last \(\frac{D}{3}\) at 40 km/h takes the remaining \(\frac{2T}{3}\): \(\frac{D}{120} = \frac{2T}{3} \Rightarrow D = 80T\).
- \(\frac{80T}{60} = T + 3.5 \Rightarrow \frac{T}{3} = 3.5 \Rightarrow T = 10.5\) hours.
- Scheduled arrival \(= 9\) am \(+ 10.5\) h \(= 7{:}30\) pm.