Question

$A$ and $B$ are both waiting for an appointment with a professor. When they arrived, each received a card from the guard, telling the hour and minute of his/her arrival. Two minutes ago, $A$ had been waiting exactly $\frac{1}{2}$ as many minutes as $B$. Three minutes from now, A will have been waiting exactly $\frac{2}{3}$ as long as $B$. If the time is now $11$:$30$, at what time did $A$ arrive?

• A. $11$:$16$
• B. $11$:$18$
• C. $11$:$20$
• D. $11$:$23$
• E. $11$:$25$

Answer 1

Answer: (D)

$11$:$23$

Solution:

Let $A$ be waiting from $x$ minutes.

and $B$ be waiting from $y$ minutes.

Present time $=11:30$

Two minutes ago,

$(x-2)=\frac{1}{2}(y-2)$

or, $2x-y=2$ ................(i)

and three minutes from now

$x+3=\frac{2}{3}(y+3)$

or, $3x-2y=-3$ .....................(ii)

Solving eqn(i) and (ii) we get,

$x=7$ and $y=12$

Therefore, $A$ is waiting from $7$ minutes

i.e. $A$ arrived $7$ minutes before $11:30$ i.e. at $11:23$

Hence, D is the correct option.