Question

MISCELLANEOUS QUESTIONS
72. A faster train takes one hour less than a slower train for a journey
of
200 km. If the speed of the slower train is 10 kmph less than that of the
faster train, find the speeds of two trains.
[CBSE 2018C]
73. A motorboat whose speed is 18 kmph in still water takes 1 hr 30 min
more to go 36 km upstream than to return downstream to the same
spot. Find the speed of the stream.
[CBSE 2019C]
74. Two pipes together can fill a tank in 12 hours. If the first pipe can fill
the tank 10 hours faster than the second then how many hours will the
second pipe take to fill the tank?
[CBSE 2019C]
75. Two water taps together fill a tank in 12 hours. The tap with longer
diameter takes 2 hours less than the tap with smaller one to fill the tank
separately. Find the time in which each tap can fill the tank separately.
[CBSE 2019]
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Answer 1

Answer:

Let speed of fast train be x km/hr

speed of slower train = x - 10 km/hr

Given fast train takes 1 hr less than slower one in covering 200 km

⇒ 200/ x = 200/x-10 - 1

⇒ 200/x = 200 - (x-10) / x-10

⇒ 200(x-10) = 200x - x (x-10)

⇒200x-2000 = 200x - x² + 10x

⇒x² - 10x - 2000 = 0

⇒ x² -50x + 40x -2000 = 0 ⇒ (x-50)(x+40) = 0

x = 50 and x= - 40

since x can't be negative , so x= speed of faster train = 50 km/hr

speed of slower train = 40 km/hr