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AP ICET 2015 Paper

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Question : 91 of 200

Marks: +1, -0

Two cars A and B start at the same time and move in opposite directions between the places x and y. The time taken by Car A and Car B to reach their destinations after they meet each other on their way is 4 hours and 9 hours respectively. Then the ratio of the speeds of cars A and B is

$3:2$
$2:3$
$9:4$
$4:9$

Solution:

Let A and B meet at Z aftert hours and their speeds be

v_A

and

v_B

respectively.

∴

v_{A}t=9v_{B}

and

v_{B}t=4v_{A}

\Rightarrow\frac{v_{A}t}{v_{B}t}=\frac{9v_{B}}{4v_{A}}

\Rightarrow\left(\;\;\frac{v_{A}}{v_{B}}\right)^{2}=\;\;\frac{9}{4}=\;\;\left(\;\;\frac{3}{2}\right)^{2}

∴

v_{A}:v_{B}=3:2

Note : The standard formula for such a case is

\frac{v_A}{v_B}=\sqrt{\frac{T_B}{T_A}}

Where

T_A

and

T_B

are respectively the time taken by A and B to reach their destinations after meeting on the way.

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