JIPMAT 2024 (QA) - Ram and Shyam run a race between points A and B, 5 ~km apart. Ram starts at 9 AM from A at a speed of 5 ~km / hr, reaches B and returns to A at the same speed. Shyam starts at 9: 45 AM from A at a speed of 10 ~km / hr, reaches B and comes back to A at the same speed. what time do Ram and Shyam meet each other ? | PYQs + Solutions

JIPMAT 2024

Arithmetic

Time, Speed & Distance

Hard

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 do Ram and Shyam meet each other ?

10: 00 \mathrm{AM}

10: 10 \mathrm{AM}

10: 20 \mathrm{AM}

10: 30 \mathrm{AM}

Correct Option: 2

According to the question, at 10:00 AM, Ram will have reached B (as his speed is 5kmph and he travelled for an hour, starting at 9 AM)

And Shyam will have reached halfway to B (He would take 30 minutes to reach B but he only travelled 15 minutes, since he started at 9:45 AM)

Now Ram is heading back towards A, hence Ram and Shyam are heading towards each other.

At 10:10 AM, 10 minutes after, Ram will have travelled

\frac{5000}{6}=833.3

m (He travels 5000 every 60 minutes, so we divide by 6 to find out how much he travelled in 10 minutes)

And Shyam will have travelled

\frac{10000}{6}=1666.6

The sum of these distances,

1666.6+833.3=2.5

km, which was the distance between them at 10:00 AM. Hence they'll meet at 10:10 AM.