NinetynineCAT 2024 Slot 1 QA Q15 Time, Speed & Distance
Question 15 of the Quantitative Ability (QA) section, CAT 2024 Slot 1, with CAT's official answer and a worked solution.
Two places A and B are 45 kms apart and connected by a straight road. Anil goes from A to B while Sunil goes from B to A. Starting at the same time, they cross each other in exactly 1 hour 30 minutes. If Anil reaches B exactly 1 hour 15 minutes after Sunil reaches A, the speed of Anil, in km per hour, is
- A16
- B14
- C12
- D18
Answer: (C) 12 Time, Speed & Distance MCQ
Solution
- They meet after 1.5 h, so the speeds add up to \(45 / 1.5 = 30\) km/h.
- Anil's total time exceeds Sunil's by 1.25 h: \(\frac{45}{a} - \frac{45}{30 - a} = 1.25\).
- Try \(a = 12\): \(\frac{45}{12} - \frac{45}{18} = 3.75 - 2.5 = 1.25\) ✓. So Anil's speed is 12 km/h.
Shortcut. Anil must be the slower one (he takes longer), so only 12 or 14 are possible; 12 checks out.