# CAT2019-2: 74

128 views

A cyclist leaves $A$ at $10$ am and reaches $B$ at $11$ am. Starting from $10:01$ am, every minute a motor cycle leaves $A$ and moves towards $B$. Forty-five such motor cycles reach $B$ by $11$ am. All motor cycles have the same speed. If the cyclist had doubled his speed, how many motor cycles would have reached $B$ by the time the cyclist reached $B$?

1. $23$
2. $20$
3. $15$
4. $22$

edited

Ans is option (C)

Let the distance between point A and point B be $d$ km. Time taken by the cyclist to cover $d$ km is $1$hr.

$\therefore$  Initial Speed of the cyclist $v_{c}=\frac{d}{1}=d$ kmph.

Now, every minute from $10:01$ A.M., a bike leaves point A, and $45$ such bikes reach point B after $1$ hr.

It is given that speed of each bike is same. So, last bike will leave at $10:45$ A.M. and reach B at $11:00$ A.M.

$\therefore$ time taken by a bike to get from point A to point B $=15$ minutes.

Now, if the cyclist doubles his speed, he will reach point B in $\frac{d}{2d}=0.5$ hr $=$ $30$ minutes. He will reach point B at $10:30$ A.M.

Now, starting from $10:01$ A.M., first bike reaches point B at $10:16$ A.M.

Second bike reaches point B at $10:17$ A.M.  and so on...till $15^{th}$ bike which starts at $10:15$ A.M. reaches point B at $10:30$ A.M.

Hence a total of $15$ bikes will reach B by the time cyclist reaches B.

238 points 2 2 4

## Related questions

1
173 views
The salaries of Ramesh, Ganesh and Rajesh were in the ratio $6:5:7$ in $2010$, and in the ratio $3:4:3$ in $2015$. If Ramesh’s salary increased by $25$% during $2010-2015$, then the percentage increase in Rajesh’s salary during this period is closest to $8$ $7$ $9$ $10$
2
94 views
If x is a real number, then $\sqrt{\log _{e}\frac{4x-x^{2}}{3}}$ is a real number if and only if $1\leq x\leq 2$ $-3\leq x\leq 3$ $1\leq x\leq 3$ $-1\leq x\leq 3$
In an examination, Rama's score was one-twelfth of the sum of the scores of Mohan and Anjali. After a review, the score of each of them increased by $6$. The revised scores of Anjali, Mohan, and Rama were in the ratio $11:10:3$. Then Anjali's score exceeded Rama's score by $24$ $26$ $32$ $35$
How many pairs $(m,n)$ of positive integers satisfy the equation $m^{2}+105=n^{2}$?____
Anil alone can do a job in $20$ days while Sunil alone can do it in $40$ days. Anil starts the job, and after $3$ days, Sunil joins him. Again, after a few more days, Bimal joins them and they together finish the job. If Bimal has done $10$% of the job, then in how many days was the job done? $14$ $13$ $15$ $12$