Calenders Q31

31. Dilip is a book worm and his wife Rama Dilip is also a voracious reader. Dilip reads at an average rate of 40 pages per hour, while Rama Dilip reads at an average rate of 50 pages per hour. Dilip starts reading a novel at 4.30 PM and Rama Dilip begins reading an identical copy of the same book at 5.20 PM. At 6.00 PM suddenly a family friend arrived and both husband and wife had to spend 30 minutes with the guest. Thereafter, they started reading again. At what time will both husband and wife will be reading the same page?

(a)10.00PM

(b) 9.30 pm

(c) 9.10 PM 

(d) 8.20Pm 

(e) 7.30 PM

Answer :  c) 9.10 PM

Explanation:

We have to find out when Rama Dilip will catch up with Dilip. Dilip reads at the rate of 40 pages per hour and Rama Dilip reads at the rate of 50 pages per hour. Dilip starts 50 minutes ahead of his wife. Since 50 minutes is 5/6 of an hour, by the time Rama Dilip starts reading at 5.20 PM, Dilip has already read 5/6 x40=200/6 pages. Please note that Rama Dilip is faster by 10 pages per hour as compared to her husband.

Since Dilip started with 200/6 pages ahead at 5.20 PM to catch up with Dilip it should take Rama Dilip 200/6 pages / 10 pages per hour. ie 200/60 hours or 3 hours 20 minutes. And of course the common time spent by both husband and wife chatting with guest is 30 minutes. So to catch up with Dilip, Rama Dilip requires 3 hours 20 minutes + 30 minutes or 3 hours 50 minutes. Rama Dilip and Dilip will be reading the same page at 5.20 PM + 3 hours 50 minutes ie by 9.10 PM.