In a circular race of 840 m, A and B start running in the same direction at the same time from the same point at the speeds of 6 m/s and 12 m/s, respectively. After how much time will they meet next?

The correct option is 140 s.

To find the time when A and B will meet next in a circular race, we can use the concept of relative speed.

Given parameters:
Length of the circular track,
$L=840\text{ m}$
Speed of A,
$v_A=6\text{ m/s}$
Speed of B,
$v_B=12\text{ m/s}$

Since both A and B start from the same point at the same time and run in the same direction, their relative speed is the difference between their individual speeds:
$v_{\text{relative}}=v_B-v_A$
$v_{\text{relative}}=12-6=6\text{ m/s}$

For them to meet again, the faster runner (B) must gain a lead of exactly one full track length (840 m) over the slower runner (A).

We calculate the time taken to cover this relative distance at their relative speed using the formula:
$\text{Time}=\frac{\text{Distance}}{\text{Relative Speed}}$
$t=\frac{840}{6}=140\text{ s}$

Therefore, A and B will meet next after 140 s.