The distance from city P to city Q is 27 km. A and B start walking from P towards Q at speeds of 5 km/hr and 7 km/hr,respectively. B reaches Q, returns immediately, and meets A at R. What is the distance between P and R?(assume all threecities to be in one straight line)

Correct option is B

Given:
Distance from City P to Q = 27 km
Speed of A = 5 km/h
Speed of B = 7 km/h
B reaches Q, returns immediately, and meets A at R
Find the distance from P to R
​
Formula Used:

$$\text{Time} = \frac{\text{Distance}}{\text{Speed}}$$

Solution:

The distance from P to Q is 27km.

Speed of A = 5 km/hr

Speed of B = 7 km/hr.

B reaches Q and returns and meets A at point R.

Let RQ be x

∴ PR = 27 - x.

∴ The time taken by A to travel 27 - x distance is same as the time taken by B to travel.

​$$\frac{27 - x}{5} = \frac{27 + x}{7} \\[5pt]\Rightarrow 7(27 - x) = 5(27 + x) \\[5pt]\Rightarrow 189 - 7x = 135 + 5x \\[5pt]\Rightarrow 12x = 54 \\[5pt]\Rightarrow x = \frac{54}{12} \\[5pt]\Rightarrow x = \frac{9}{2} = 4.5 \\[5pt]\therefore 27 - x = 27 - 4.5 = \boxed{22.5\ \text{km}}$$​​

The distance between P and R is 22.5.