76. Rajdhani Express leaves Mumbai ...
Question

# 76. Rajdhani Express leaves Mumbai towards Delhi at 3.10 p.m. and travels uniformly at 120 kmph. August Kranti Express leaves Delhi towards Mumbai at 12.20 p.m. and travels uniformly at 80 kmph. Both trains cross at Baroda at 4.30 p.m. On a particular day, Rajdhani Express leaves at 3.20 p.m. when will the two trains cross ? a. 4.32 pm b 4.36 pm c. 4.28 pm d 4.40 pm

Railway Exams
Maths
Solution
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Both trains have uniform speeds. .. but do not travel the same length of time. The AKR Express leaves at ( 12: 20 mathrm{pm} ) and crosses Baroda at ( 4: 30 mathrm{pm} ). It travels for ( 4 frac{1}{6} ) hours at ( 80 mathrm{km} / mathrm{hr} ). Its distance is: ( left(frac{25}{6}right)(80)=frac{1000}{3} mathrm{km} ) The R Express leaves at 3: 10 and crosses Baroda at 4: 30 pm. It travels for ( 1 frac{1}{3} ) hours at ( 120 mathrm{km} / mathrm{hr} ). Its distance is: ( left(frac{4}{3}right)(120)=160 mathrm{km} ) The total distance is: ( frac{1000}{3}+160=frac{1480}{3}=493 frac{1}{3} mathrm{km} ) On that particular day, AKR Express has a three-hour headstart. From 12: 20 pm to 3: 20 pm, it has travelled: ( 3 times 80=240 ) km already. At ( 3: 20 mathrm{pm}, ) the trains have a combined speed of ( 200 mathrm{km} / mathrm{hr} ) to cover the remaining ( frac{1480}{3}-240=frac{760}{3} mathrm{km} ) The time required is: ( frac{frac{760}{3}}{200}=frac{760}{600}=frac{76}{60} ) hours ( =1 ) hour, 16 minutes Therefore, the trains meet 1 hour, 16 minutes after 3: 20 pm ( ldots ) at 4: 36 pm.