At 10:45 Shyam finishes race and at 11 Ram also finishes rt?

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**Answer the question based on the information given below.**

Ran and Shyam run a race between points A and B, $5$ km apart. Ram starts at $9$ a.m. from A at the speed of $5$ km per hour, reaches B and returns to A at the same speed. Shyam starts at $9:45$ a.m. from A at the speed of $10$ km per hour, reached B and come back to A at the same speed.

At what time did Shyam overtake Ram?

- $10:20$ a.m.
- $10:30$ a.m.
- $10:40$ a.m.
- $10:50$ a.m.

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At the point of overtake, distance travelled by Ram and Shyam must be the same.

So, if this is assumed as $t$ hours after 9:00, we have

$5 \times t = 10 \times \left(t- \frac{45}{60} \right)$

$\implies 20 t = 40t - 30$

$\implies t = \frac{3}{2}$

So, after 1.5 hrs from 9:00 i.e., at 10:30 Shyam overtakes Ram.

So, if this is assumed as $t$ hours after 9:00, we have

$5 \times t = 10 \times \left(t- \frac{45}{60} \right)$

$\implies 20 t = 40t - 30$

$\implies t = \frac{3}{2}$

So, after 1.5 hrs from 9:00 i.e., at 10:30 Shyam overtakes Ram.