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CAT 2022 Slot 1 Paper

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Question : 49 of 66

Marks: +1, -0

Trains $A$ and $B$ start traveling at the same time towards each other with constant speeds from stations $X$ and $Y$ , respectively.Train $A$ reaches station $Y$ in 10 minutes while train $B$ takes 9 minutes to reach station $X$ after meeting train $A$ . Then the total timetaken, in minutes, by train $B$ to travel from station $Y$ to station $X$ is

6
15
10
12

Solution:

M

- First meeting point

Let the speeds of trains

A

and

B

be '

a

' and '

b

', respectively.

\frac{x}{a}=\frac{D-x}{b}

It is given,

rac{D}{a}=10

and

rac{x}{b}=9

\frac{x}{\frac{D}{10}} = \frac{D-x}{\frac{x}{9}}

\frac{10x}{D}=\frac{9D-9x}{x}

10x^2=9D^2-9Dx

10x^2+9Dx-9D^2=0

Solving, we get

x=\frac{3D}{5}

rac{x}{b}=9

rac{3D}{b imes 5}=9

rac{D}{b}=15

The total time taken by train

B

to travel from station

Y

to station

X

is 15 minutes.

The answer is option B

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