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asked 2016-08-20 23:17:18 
Pathik and Rahi started from two places Andheri and Bhavnagar towards Bhavnagar and Andheri respectively at $8:20$ am. The speeds of Pathik and Rahi are in the ratio $4:5.$ They meet at Chandni Chowk, somewhere between Andheri and Bhavnagar, spent some time together for coffee and burger and then both started towards their destination at $9:27$ am. If Pathik reaches Bhavnagar at $10:32$ am, how much time did they spend together?
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answered 2016-08-21 09:14:22 
Ans: $15$ minutes

Time taken by Pathik to travel from the meeting point to Bhavnagar,
$=10:32\text{ am}-9:27\text{ am}=1\text{ hr }5 \text{ min}$

Speed of Pathik and Rahi $=4:5$

Since time is inversely proportional to speed, time taken by Rahi to travel from Bhavnagar to the meeting point
$=(1\text{ hr }5 \text{ min})×\dfrac{4}{5}=48+4=52\text{ min}$

therefore, time at which they both reached the meeting point
$=8:20\text{ am}+52\text{ min}=9:12\text{ am}$

Time that they spent together for coffee and burger
$=9:27\text{ am}-9:12\text{ am}=15\text{ minutes}$
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