Question

plz give me answer fast

Answer 1

AnswEr

The correct option is

c) 40 km/hr

Given

• The total distance travelled by train is 360km
• If the speed of train is 5km/h more the journey takes 1hour less .

To Find

• The speed of the train

Solution

Let us consider the speed of the train be x km/h

We know that

speed = distance/time

⇒ x = 360/t _____(1)

and

⇒ x + 5 = 360/(t - 1)

⇒ x = 360/(t - 1) - 5

⇒ x ={360 - 5(t - 1)}/(t-1)_____(2)

Comparing (1) and (2) we have

⇒ 360/t =( 360 - 5t + 5)/(t - 1)

⇒ 360(t - 1) = t( 365 - 5t)

⇒360t - 360 = 365t - 5t²

⇒ -5t² + 5t + 360 = 0

⇒ 5t² - 5t - 360 = 0

⇒ 5(t² - t - 72) = 0

⇒ t² - t - 72 = 0

⇒ t² + 8t - 9t - 72 = 0

⇒ t(t + 8) - 9(t + 8) = 0

⇒ (t - 9)(t + 8)

Therefore ,

t - 9 = 0 or t + 8 = 0

⇒ t = 9 or⇒ t = -8

Since time can never be negative so t ≠ -8

Thus time taken is 9 hours

Since speed = distance/time

⇒ x = 360/9

⇒x = 40

The speed of the train is 40km/h

Answer 2

$\Large{\underline{\underline{\mathfrak{\bf{\red{Question}}}}}}$

A train travels 360 km at a uniform speed .

If the speed had been 5 km/h more, it would have taken 1 hours less for the same journey . Find the speed of train ?

$\Large{\underline{\underline{\mathfrak{\bf{\red{Solution}}}}}}$

$\Large{\underline{\mathfrak{\bf{\pink{\Given}}}}}$

• Train have complete total distance in own journey = 360 km
• If train had been 5 km more, then its have take 1 hours less to complete same journey .

$\Large{\underline{\mathfrak{\bf{\pink{Given}}}}}$

• Speed of train .

$\Large{\underline{\underline{\mathfrak{\bf{\blue{Explanation}}}}}}$

Let,

$:\mapsto\sf{\orange{\:speed_{Train}\:=\:S\:km/h}} \\ \\ \\ :\mapsto\sf{\orange{\:Time\:=\:t}}$

$\small{\underline{\mathfrak{\bf{\pink{Relation\:between\:speed,\:time\:and\:distance}}}}}$

$\boxed{\underline{\sf{\green{\:Speed_{Train}\:=\:\dfrac{Distance}{Time}}}}}$

$:\mapsto\sf{\:Speed_{Train}\:=\:\dfrac{360}{t}} \\ \\ \\ :\mapsto\sf{\green{\:S\:=\:\dfrac{360}{t}}.........(1)}$

Again, A/C to question,

( If train had been 5 km more, then its have take 1 hours less to complete same journey . )

Here,

• speed (S) = S + 5 km/h
• time (t) = (t-1) h

$:\mapsto\sf{\:(S+5)\:=\:\dfrac{360}{(t-1)}} \\ \\ \\ :\mapsto\sf{\:S\:=\:\dfrac{360}{(t-1)}\:-\:5} \\ \\ \\ :\mapsto\sf{\:S\:=\:\dfrac{360-5(t-1)}{(t-1)}......(2)}$

Substitute value of S by equ(1)

$:\mapsto\sf{\:\dfrac{360}{t}\:=\:\dfrac{360-5(t-1)}{(t-1)}} \\ \\ \\ :\mapsto\sf{\:360.(t-1)\:=\:360t-5t(t-1)} \\ \\ \\ :\mapsto\sf{\:5t^2-5t+\cancel{360t-360t}-360\:=\:0} \\ \\ \\ :\mapsto\sf{\:5t^2-5t-360\:=\:0} \\ \\ \\ \small\sf{\green{\:\:\:\:\:take\:5\:common}} \\ \\ \\ :\mapsto\sf{\:5(t^2-t-72)\:=\:0} \\ \\ \\ :\mapsto\sf{\:(t^2-t-72)\:=\:0} \\ \\ \\ \small\sf{\green{\:\:\:\:\:factories\:of\:this\:equation}} \\ \\ \\ :\mapsto\sf{\:(t^2-9t+8t-72)\:=\:0} \\ \\ \\ :\mapsto\sf{\:t(t-9)+8(t-9)\:=\:0} \\ \\ \\ :\mapsto\sf{\:(t-9)(t+8)\:=\:0} \\ \\ \\ :\mapsto\sf{\:(t-9)\:=\:0\:\:Or\:\:\:(t+8)\:=\:0} \\ \\ \\ :\mapsto\sf{\:t\:=\:9\:\:Or\:\:t\:=\:-8}$

Since,

Time be not negative

• t ≠ -8

So, Take t = 9

Keep value of t in equ(1),

$:\mapsto\sf{\:Speed_{Train}\:=\:\cancel{\dfrac{360}{9}}} \\ \\ \\ :\mapsto\sf{\red{\:Speed_{Train}\:=\:40\:km/h}}$

This is required speed of train .

$\Large{\underline{\mathfrak{\bf{\pink{Hence}}}}}$

• Answer will be options number (C).

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