Q. |
Four persons - Ahmed, Burman, Chhaya, and Deepak, in that order, occupy the four corners of a square of side $a$ in clockwise order. Ahmed and Burman start walking simultaneously towards Burman and Chhaya respectively along the edges of the square. Both stop walking when Burman reaches Chhaya. Now, if the distance between Ahmed and Burman is $a/2$, which of the following statements must be false? |
✔ A. | Ahmed has walked a distance of only $3a/2$ |
✖ B. | Ahmed walks faster than Burman. |
✖ C. | Ahmed might have walked for a distance of more than $2a$ |
✖ D. | Ahmed might have to travel a distance of $3a/2$ more to get back to his original position. |
Solution:
Option(A) is correct
Refer the diagram,
Here, A, B, C and D represent the starting positions of Ahmad, Burman, Chhaya and Deepak respectively such that AB = BC = CD = DA $= a$
B’ is the final position of Burman and A’ or A’’ are the two possible final positions of Ahmad such that B’A’ = B’A’’ $= a/2$
Now, the distance walked by Ahmed is either $3a/2$ or $5a/2$
Consider option A: Ahmed has walked a distance of only $3a/2$.
The word only has made this statement ‘must be false’.
Hence, option A is the correct choice..