Question

Two persons 'A' and 'B' walk round a circle whose 0diameter is 1.4 km. A walks at a speed of 100 meters per minute while B walks at a speed of 110 meters per minute. If they both start at the same time, from the same point and walk in the same direction, at what interval of time would they both be at the same starting point again?​

Answer 1

Answer:

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Answer 2

$\large\underline{\sf{Solution-}}$

Given that

Diameter of circle, d = 1.4 km = 1.4 × 1000 = 1400 m

So, we know

$\underbrace{\boxed{ \tt{Circumference_{(circle)} = \pi \: d}}}$

So,

$\rm :\longmapsto\:Circumference_{(circle)} \: = \dfrac{22}{7} \times 1400 = 4400 \: m$

Now, Further given that

Speed of A = 100 meters per minute.

and

Speed of B = 110 meters per minute

We know that,

$\underbrace{\boxed{ \tt{Time = \frac{Distance}{Speed} }}}$

So, time taken by A to cover 4400 km at a speed of 100 meters per minute is

$\rm \:  =  \:  \: \dfrac{4400}{100} = 44 \: min$

and

Time taken by B to cover 4400 km at a speed of 110 meters per minute is

$\rm \:  =  \:  \: \dfrac{4400}{110} = 40 \: min$

So, we have now,

Time taken by A for one complete round = 44 min

Time taken by B for one complete round =40 min

Now, to find the time after what interval they will be at same starting point, we have to find LCM ( 44, 40 ).

Now,

$\begin{gathered}\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{2}}}&{\underline{\sf{\:\:44\:, \: 40 \:\:}}}\\ {\underline{\sf{2}}}& \underline{\sf{\:\:22\:, \: 20 \:\:}} \\\underline{\sf{10}}&\underline{\sf{\:\:11\:, \: 10 \:\:}}\\ {\underline{\sf{11}}}& \underline{\sf{\:\:11\:, \: 1 \:\:}}\\\underline{\sf{}}&{\sf{\:\:1\:, \: 1 \:\:}} \end{array}\end{gathered}\end{gathered}\end{gathered}$

So, LCM ( 44, 40 ) = 2 × 2 × 10 × 11 = 440 minutes

We know, 60 minutes = 1 hour

So, 440 minutes = 7 hours and 20 minutes.

So,

They will be at same starting point after 7 hour 20 min.

Additional Information :-

If a and b are two positive integers having HCH h and LCM l then

1. HCF × LCM = a × b

2. HCF always divides a, b and LCM

3. HCF of a and b is always less than or equals to a or b.

4. LCM of a and b is always greater than or equals to a or b.