Question

Two friends a and b simultaneously start running around a circular track. they run in the same direction. a travels at 6 m/s and b runs b m/s. if they cross each other at exactly two points on the circular track and b is a natural number less than 30, how many values can b take?

Answer 1

$\huge\textbf{Solution}$
Let distance of the circular track =d metre.

Relative speed =(6−b)m/s or (b−6)m/s

Time taken to meet first time

$= \frac{d}{6 - b} sec \: \: or \frac{d}{b - 6} sec$
Time taken by A to complete one round =d/6 sec
.

Time taken by B to complete one round =d/b sec

Since they cross each other at exactly two points on the circular track, second time they meet exactly at the starting point. 

$= LCM( \frac{d}{6} , \frac{d}{b} ) \\ \\ = \frac{LCM(d,d)}{HCF(6,b)} \\ \\ = \frac{d}{HCF(6,b)}$

Therefore

$= \frac{ \frac{d}{HCF(6,b) } }{ \frac{d}{6 - b} } \\ \\ = 2$
Or

$\frac{ \frac{d}{HCF(6,b)} }{ \frac{d}{b - 6} } \: \\ \\ = 2$
$\frac{6 - b}{HCF(6,b) } = 2$
or

$\frac{b - 6}{HCF(6,b) } = 2 =...........(1)$

b=2,10,8

satisfies (1)

Therefore, b can take 33 values

Thanks a lot

Have a colossal day ahead

Be Brainly

Answer 2

Small farmers keep substantial share of production for their own family needs. Only 25% of the people working in Rampur are engaged in activities other than agriculture such as dairy farming, small scale manufacturing, shop-keeping and transport. MNREGA has provided some support to the incomes of rural workers.