Anand and Bala started from towns P and Q simultaneously towards Q and P respectively. After 6 hours, they crossed each other at town R. After that, Anand took 5 hours more to reach Q than Bala took to reach P. Find the sum of the times taken by them to reach their destinations from R (in hours).
Let the distance from P to Q and R to Q be x and y km respectively.
Let the time taken by Bala from R to P be h hours. So, the time taken by Anand from R to Q will be h+5 hours.
Bala's speed = \(\frac{distance}{time}\)
\(= \frac{y}{6} = \frac{x}{h} ---> x = \frac{yh}{6}\)
Anand's speed = \(\frac{distance}{time} \)
\(= \frac{x}{6} = \frac{y}{h+5} ---> \frac{yh}{36} = \frac{y}{h+5}\)
\(\frac{h}{36} = \frac{1}{h+5}\)
\(h^2 + 5h = 36\)
\(h^2 + 5h - 36 = 0\)
\((h+9)(h-4) = 0\)
h=4
Sum of the times taken by them to reach their destinations from R (in hours) = h + (h + 5) = 13 hours.
Choice b is the answer.
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