Question:
Rahim drives from city A to station C at \(70\) km/h. Train leaves city B (500 km south of A) at 8:00 am toward C at \(50\) km/h. C is located between S and SW of A with AC at \(30^\circ\) to AB. Rahim must reach C at least 15 minutes before train. Latest time to leave A?
Rahim drives from city A to station C at \(70\) km/h. Train leaves city B (500 km south of A) at 8:00 am toward C at \(50\) km/h. C is located between S and SW of A with AC at \(30^\circ\) to AB. Rahim must reach C at least 15 minutes before train. Latest time to leave A?
Show Hint
Relative motion problems with angled paths can be solved by breaking into components using trigonometry.
Updated On: Jul 30, 2025
- 6:15 am
- 6:30 am
- 6:45 am
- 7:00 am
- 7:15 am
Hide Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
AC forms \(30^\circ\) with AB (500 km). Distance AC = \(500 / \cos 30^\circ \approx 577.35\) km.
Train’s path: BC = 500 km \(\tan 30^\circ \approx 288.675\) km offset → BC length from geometry.
Train speed 50 km/h, Rahim 70 km/h. Compute times to meet at C, ensuring Rahim arrives 15 min earlier.
Latest start time from A ≈ 6:30 am.
Was this answer helpful?
0
0
Top Questions on Relative Speed
- Two sisters Neha and Monica walk to school from the house. Neha takes 40 minutes while Monica takes 30 minutes. One day Neha started 5 minutes earlier than Monica. In how many minutes would Monica overtake Neha?
Cities A and B are in different time zones. A is located \(3000 \ \text{km}\) east of B. The table below describes the schedule of an airline operating non-stop flights between A and B. All the times indicated are local and on the same day.
Departure City Time Arrival City Time B 8:00 am A 4:00 pm A 3:00 pm B 8:00 pm Assume that planes cruise at the same speed in both directions. However, the effective speed is influenced by a steady wind blowing from east to west at \(50 \ \text{km/h}\).
- CAT - 2007
- Quantitative Aptitude
- Relative Speed
- Arun, Barun, and Kiranmala start from the same place and travel in the same direction at speeds of 30, 40, and 60 km/h respectively. Barun starts two hours after Arun. If Barun and Kiranmala overtake Arun at the same instant, how many hours after Arun did Kiranmala start?
- CAT - 2006
- Quantitative Aptitude
- Relative Speed
Ram and Shyam run a race between points A and B, 5 km apart. Ram starts at 9:00 a.m. from A at a speed of 5 km/hr, reaches B, and returns to A at the same speed. Shyam starts at 9:45 a.m. from A at a speed of 10 km/hr, reaches B, and comes back to A at the same speed.
- CAT - 2005
- Quantitative Aptitude
- Relative Speed
- Two places P and Q are 120 km apart from each other on a highway. A car starts from P and another from Q at the same time. If they move in the same direction, they meet each other in 8 hours. If they move in opposite directions towards each other, they meet in 2 hours 40 minutes. What are the respective speeds of the cars in km/hour?
- Quantitative Aptitude
- Relative Speed
Questions Asked in CAT exam
- Suppose $x_1, x_2, x_3, \dots, x_{100}$ are in arithmetic progression such that $x_5 = -4$ and $2x_6 + 2x_9 = x_{11} + x_{13}$. Then, $x_{100}$ equals ?
- CAT - 2024
- Arithmetic Progression
- A circular plot of land is divided into two regions by a chord of length $10\sqrt{3}$ meters such that the chord subtends an angle of $120^\circ$ at the center. Then, the area, in square meters, of the smaller region is
- CAT - 2024
- Mensuration
- For some constant real numbers p, k and a, consider the following system of linear equations in x and y:
px - 4y = 2
3x + ky = a
A necessary condition for the system to have no solution for (x, y), is- CAT - 2024
- System of Linear Equations
- When 3333 is divided by 11, the remainder is
- CAT - 2024
- Divisibility and Remainder
- Five jumbled up sentences (labelled 1, 2, 3, 4 and 5), related to a topic, are given below. Four of them can be put together to form a coherent paragraph. Identify the odd sentence and key in the number of that sentence as your answer.
- CAT - 2024
- Para Jumbles
View More Questions