Ram and Shyam run a race between points $A$ and $B, 5 \mathrm{~km}$ apart. Ram starts at 9 AM from $A$ at a speed of $5 \mathrm{~km} / \mathrm{hr}$, reaches $B$ and returns to $A$ at the same speed. Shyam starts at $9: 45 \mathrm{AM}$ from $\mathrm{A}$ at a speed of $10 \mathrm{~km} / \mathrm{hr}$, reaches $B$ and comes back to $A$ at the same speed. At what time does Shyam overtake Ram ?
Solution
✅ Correct Option: 2
As we know from the previous question, Shyam will have reached B at 10:15 AM, and Ram would have travelled $\frac{5}{4}=1.25$km back to A from B at that time. Let's go by the options in ascending order of time. At 10:20 AM, 5 minutes after 10:15 AM, Shyam will have travelled $\frac{10000}{12}=833.3$m from B, back to A. (He travels 10000m every 60 minutes, divide by 12 to find how much he travels in 5 minutes) and Ram will have travelled $1250+\frac{5000}{12}=1250+416.6=1666.6$m towards A from B. Shyam still hasn't overtaken Ram. Let's check for 10:30 AM, 10 minutes later. At 10:30 AM, Shyam will have travelled $833.3+\frac{10000}{6}=833.3+1666.6=2500$m and Ram will have travelled $1666.6+\frac{5000}{6}=1666.6+833.3=2500$m At 10:30 AM, Shyam has caught upto Ram, but since he is faster than him, he will overtake Ram this minute itself. Hence, Shyam overtakes Ram at 10:30 AM.