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 does Shyam overtake Ram ? | PYQs + Solutions

JIPMAT 2024

Arithmetic

Time, Speed & Distance

Medium

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 ?

10: 20 \mathrm{AM}

10: 30 \mathrm{AM}

10: 40 \mathrm{AM}

10: 50 \mathrm{AM}

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

\newline

Ram will have travelled

1666.6+\frac{5000}{6}=1666.6+833.3=2500

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.

JIPMAT 2024 (QA) PYQs

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