दो रेलगाड़ियों जिनकी लम्बाई क्रमश: 100 मीटर तथा 95 मीटर है समान दिशाओ में चलते हुए एक दूसरे को पर करने में 27 सेकंड का समय लेती है । परन्तु वह विपरीत दिशाओ में चलते तो पार करने में केवल 9 सेकंड का समय लेती है । प्रत्येक रेलगाड़ी की चाल बताए ?

Options

A. 44 km/hr, 22 km/hr
B. 52 km/hr , 26 km/hr
C. 36 km/hr ,18 km/hr
D. 40 km/hr, 18 km/hr

Answer

B

Explanation

(b)Let the speed of first train be `s_(1)` km/hr and speed of second train is `s_(2)` km/hr (माना की पहल तथा दूसरे ट्रैन की चाल क्रमश :) `s_(1)`km/hr और `s_(2)` km/hr है )
As we know that ,
Time `=("total distance")/(("relative speed in same/opp. direction "))`
In the same direction.
`implies 27 sec =((100+95))/((s_(1)-s_(2))xx(5)/(18))`
`implies 27=(195xx18)/((s_(1)-s_(2))xx5)`
`implies s_(1)-s_(2)=26`.........(i)
In the oppo. direction (विपरीत दिशा में )
`implies9=((10+95))/(s_(1)+s_(2))xx(5)/(18) implies 9=(195xx18)/((s_(1)+s_(2))xx5)`
`implies s_(1) + s_(2) = 39 xx 2`
`implies s_(1) + s_(2) = 78" "...(iii)`
From equation (i) and (ii)
`implies s_(1) - s_(2)=26`
`implies s_(1) + s_(2)=78`
`implies s_(1) =(26+ 78)/(2) implies s_(1)=(104)/(2)`
`implies s_(1) = 52` km/hr and `s_(2) =26` km/hr