Therefore, , Let A takes x hours to fill then B will take x-8 hr , 20x-96= -8x -28x+96=0 x= 24 hr (because x cannot be 4 hr ) Example 8. If a car can finish a journey in 10 hr with a speed of 48 kmph . The by how much the speed be increased to cover the same distance in 8 hr? Solution: Distance = speed time = 48 10 = 480 km To cover the same distance in 8 hr . Speed = d/t = 480 / 8 = 60 kmph Therefore, speed must be increased by 60-48 = 12 kmph . Example 9. A man gets late by 2 hr if he walks ¾ th of his normal speed. What time will he take to cover the same distance at his normal speed? Solution: let his normal speed be s kmph and normal time be t hr Distance, d = st = s (t+2) Or, 4t = 3t + 6 , t = 6 hr . Example 10 . The speed of A and B are in ratio 4:5. A takes 40 min more than b to cover the same distance. How much time does A take to cover this distance? Solution. Since the ratio of speed is 4 : 5 , so the ratio of time will be 5 : 4 . Facebook Group: Indian Administrative Service ( Raz Kr)
CSAT Comprehensive Page 224 Page 224 CSAT Comprehensive If it takes 40 min more , then 5x-4x = 40 x = 40 min A takes 5 x min or 5 40 = 200 min. Example 11. A man goes a hill at 20 kmph and comes down at 32 kmph along the same path. What is his average speed? Solution : Average speed = Example12. A train travelling at the rate of 72 kmph crosses a pole in 8 seconds . What is its length? Solution: time = 8 secs Speed = 72 kmph = 72 m/s = 20 m/s Length = s t = 8 20 = 160 m. Example 13. A 200 m long train crossed a 700 m long platform in 1 in 6 seconds . What is the speed of the train (in kmph ) ? Solution : Total length to be covered = length of the train + length of the platform = 200+ 700 = 900 Tota time = 60+6 = 66 min Speed = distance / time = 900/66 = 450/33 m/s = kmph. Example 14. If a boy walks from his house at 5 kmph , he reaches school 5 min early , and if he walks at 4 kmph he reaches 5 min late . How far does he work for his school? Solution : let his normal speed be x kmph . Let his normal time t hr. D = st 5 ( t - )= 4 ( t + ) 5t - = 4t + t = hr Distance = 5 ( ) = 41 km Example 15. Two train travel in opposite direction one at 30 kmph and the other at 42 kmph. A man sitting in the slower train passes the faster train in 6 s. what is the length of the faster train? Facebook Group: Indian Administrative Service ( Raz Kr)
CSAT Comprehensive Page 225 Page 225 CSAT Comprehensive Solution : since the train are running in opposite direction , hence the length of the faster train = ( 30+42 ) 6 m = 72 = 120 m Example 16. A river runs at 3 kmph . if the time taken by a man to row his boat upstream is twice the time taken by him to row it downstream , then at what speed can he row his boat in still water ? Solution : let x be the speed of the boat in still water and speed of the river = 3 kmph Speed upstream = x- 3 kmph Speed downstream = x+3 kmph (x-3 )2t = ( x+ 3 ) t 2 ( x- 3) = x+ 3 X= 9 kmph. Example 17. A train passes a pole in 20 s and crosses a platform of 200 m long in 60 s . find the length of the train ?
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