The distance from {B} to {C} is thrice that from {A} to {B}. Two trains travel from {A} to {C} via {B}. The speed of train 2 is double that of train 1 while traveling from {A} to {B} and their speeds are interchanged while traveling from B to {C}. The ratio of the time taken by train 1 to that taken by train 2 in travelling from {A} to {C} is

CAT 2020 Exam Shift 2 Solved Paper

Question : 69 of 76

Marks: +1, -0

The distance from

{B}

{C}

is thrice that from

{A}

{B}

. Two trains travel from

{A}

{C}

via

{B}

. The speed of train 2 is double that of train 1 while traveling from

{A}

{B}

and their speeds are interchanged while traveling from B to

{C}

. The ratio of the time taken by train 1 to that taken by train 2 in travelling from

{A}

{C}

Solution:

Given,

Let the speed of train 1 from

A

B

be s.
Then the speed of train 2 from

A

B

2 s

.
Time taken by train 1 to cover

{A}

{C}=\;{D}/{ {s}}+\;{3 D}/{2 {s}}=\;{5 {D}}/{2 {s}}

And, time taken by train 2 to cover

A

C

=\;{D}/{2 s}+\;{3 D}/{s}=\;{7 D}/{2 s}

Required ratio

=\;{5 D}/{2 s}: \;{7 D}/{2 s} ⇒ 5: 7

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