Question

Class 9th, Physics.

Rohit and Mohit run 5 km race on a 400 m athletics track. Rohit runs the distance in 25 minutes while Mohit takes 20 minutes. If they start from the same point simultaneously and run in the same sense, how many times will Mohit overtake Rohit during the race?

a) 1
b) 2
c) 3
d) 4
________________
$\bf { Answer \; : \; [b.] \; 2}$
Please give the answer with proper explanation ; step by step solution required!​

Answer 1

Answer:

Total no. of laps = 5000/400 = 12.5

________

Now, time taken by Mohit to complete one lap = 20 min

Time taken by Rohit to do so = 25 min

∴ Mohit takes 5 min less than Rohit to complete a lap. (25 min - 20 min = 5 min.)

So, again after 4 rounds by Rohit, Mohit will meet him at the initial point and thus will overtake him. [5 × 4 = 20 min.] But till then Mohit will already cover 5 rounds.

Again, after 5 rounds, Mohit will overtake him like he did before.

After that Mohit may not be able to overtake him as he will already complete his 12.5 laps.

________

ALITER:

_______

Time taken by Mohit to complete one lap = 20 min

Time taken by Rohit to do so = 25 min

∴ They'll meet again in = LCM(20, 25) min

20 = 2² × 5

25 = 5²

=> LCM = 2² × 5² = 100 min.

That is, when Mohit will cover 5 rounds (100 min / 20 min) & Rohit will cover 4 rounds (100 min / 25 min).

_______

Logically, again they'll meet after another 100 min. But then they will never meet as they'll already complete the race.

[Mohit will already complete his 10 rounds till then and he will have only 2.5 rounds to complete the race. That means he needs another 2.5 rounds to overtake him thrice.]

So, Mohit will overtake Rohit 2 times. Reply if any blunder has been noticed. :)

Answer 2

Question:-

Rohit and Mohit run 5 km race on a 400 m athletics track. Rohit runs the distance in 25 minutes while Mohit takes 20 minutes. If they start from the same point simultaneously and run in the same sense, how many times will Mohit overtake Rohit during the race?

a) 1

b) 2

c) 3

d) 4

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Required Answer:-

$\bullet\small\sf{Total \:no.\: of\: laps = \dfrac{5000}{400} = 12.5}$

Now, time taken by Mohit to complete one lap = $\rm{20\: min}$

Time taken by Rohit to do so = $\rm{25\: min}$

∴ Mohit takes 5 min less than Rohit to complete a lap. $\tt{(25\: min - 20\: min = 5\: min.)}$

So, again after 4 rounds by Rohit, Mohit will meet him at the initial point and thus will overtake him. $\tt{[5 × 4 = 20\: min.]}$ But till then Mohit will already cover 5 rounds.

Again, after 5 rounds, Mohit will overtake him like he did before.

After that Mohit may not be able to overtake him as he will already complete his 12.5 laps.

ALITER:

Time taken by Mohit to complete one lap = $\rm{20\: min}$

Time taken by Rohit to do so = $\rm{25\: min}$

∴ They'll meet again in = LCM(20, 25) min

$\sf{20 = 2^2 × 5}$

$\sf{25 = 5^2}$

$\sf :\implies{LCM = 2^2 × 5^2 = 100\: min.}$

That is, when Mohit will cover 5 rounds $\tt{(\dfrac{100 \:min}{ 20\: min}})$ & Rohit will cover 4 rounds $\tt{(\dfrac{100 \:min}{ 25\: min}})$ .

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[Mohit will already complete his 10 rounds till then and he will have only 2.5 rounds to complete the race. That means he needs another 2.5 rounds to overtake him thrice.]

So, Mohit will overtake Rohit 2 times.

• Hence option (b) 2 is the right answer.

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