Question : A and B start moving from places X to Y and Y to X, respectively, at the same time on the same day. After crossing each other, A and B take $5 \frac{4}{9}$ hours and 9 hours, respectively, to reach their respective destinations. If the speed of A is 33 km/hr, then the speed (in km/hr) of B is:
Option 1: 22
Option 2: 2
Option 3: $25 \frac{2}{3}$
Option 4: $24 \frac{1}{3}$
Correct Answer: $25 \frac{2}{3}$
Solution :
Speed of A = 33 km/hr
After crossing each other,
Time taken by A to reach destination = $\frac{49}{9}$ hours
Time taken by B to reach destination = 9 hours
Let the speed of B be v km/hr.
Let both A and B meet at point Z after t hours.
The time taken by A and B to cover XZ is t hrs and 9 hrs respectively.
Now, Speed = $\frac{\text{Distance}}{\text{Time}}$
⇒ XZ = 33 × t = v × 9 ----(1)
Similarly, the Time taken by A and B to cover YZ is $\frac{49}{9}$ hours and t hours respectively.
⇒ YZ = $\frac{49}{9}$ × 33 = v × t ----(2)
Dividing (1) by (2), we get,
$\frac{33\text{t}}{(\frac{539}{3})} = \frac{9\text{v}}{\text{vt}}$
⇒ t
2
= 9 × ($\frac{49}{9}$)
⇒ t = $\sqrt{49}$
$\therefore$ t = 7 hours
Substituting t in (1), we get
33 × 7 = v × 9
$\therefore$ v = $\frac{77}{3}$ km/hr = $25\frac{2}{3}$ km/hr
Hence, the correct answer is $25\frac{2}{3}$ km/hr.
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