Akshara and Siddharth travel from point P to Q, a distance of 72 km at a rate of 8 km/h and 10 km/h, respectively. Siddharth reaches Q first and returns immediately and meets Akshara at R. Find the distance from P to R.
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 64 km.
PQ = 72 km
They are meeting at point R, which means within the same time A travels PR and B travels PQ + QR.
When time is the same, the distance traveled is proportional to speed,
PR/(PQ + QR) = 8/10
⇒ (PQ - RQ)/(PQ + QR) = 8/10
⇒ 360 - 5RQ = 288 + 4RQ
⇒ 9RQ = 72
⇒ RQ = 8 km
So, PR = PQ - RQ = 72 - 8 = 64 km
Therefore, the distance between P and R is 64 km.