CAT 2020 Exam Shift 2 Solved Paper

Question : 64 of 76

Marks: +1, -0

Two circular tracks

{T} 1

and

{T} 2

of radii

100 {m}

and

20 {m}

, respectively touch at a point

{A}

. Starting from

{A}

at the same time, Ram and Rahim are walking on track

{T} 1

and track

{T} 2

at speeds

15 {km} \/ {hr}

and

5 {km} \/ {hr}

respectively. The number of full rounds that Ram will make before he meets Rahim again for the first time is

Solution:

Time taken by each of them to complete one round

=\;{\;\text " Circumference of the circle "\;}/{\;\text " speed "\;}

Time taken for Ram to cover one round

=\;{2 π × 100}/{15 × 5{/}18}=48 π

Time taken for Rahim to cover one round

=\;{2 π × 20}/{5 × 5 {/} 18}=28.8 π

Time taken by Ram and Rahim meet each other for the first time

=L C M

48 π

and

28.8 π=144 π

∴

Number of rounds made by Ram before he meets Rahim for the first time

=\;{144 π}/{48 π}=3

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