Answer: Option B
:
B
Approach 1: Convetional :
(b) Time taken by A in covering (27-x) km is same as time taken by Bin covering (27+x) km.
$\frac{27-x}{5}=\frac{27+x}{7}$
$x=\frac{27}{6}$
$\therefore XZ=27-\frac{27}{6}=27\times \frac{5}{6}=22.5km.$
Approach 2 : Alternate Approach (Using Ratios):
The total distance they will have to travel will be 2d or 54 kms. As their speeds are in the ratio of 5:7 the distances will also be in the same ratio. Hence,54 kms will have to be split in the ratio of 5:7. (i.e.,)22.5 and 41.5,hence they will meet at 22.5km.
Approach 3 : Going from answer options :
The total distance they will have to travel will be 2d or 54kms.
Now,going by the answer options :
Let us assume 25 to be the right option. Hence,A will take 5 hrs in the same time B would have covered a distance of 35 kms.hence the total distance covered will be 60,which is not what is given in the question (we need to get 54.)
Now assume 22.5 to be the right answer,hence A will take 4.5 hrs in the same time B would have covered a distance of 31.5kms,the tally of which is 54 hence that is the right option.