search
Log In
Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true
0 votes
125 views

Two ants $A$ and $B$ start from a point $P$ on a circle at the same time, with $A$ moving clock-wise and $B$ moving anti-clockwise. They meet for the first time at $10:00$ am when $A$ has covered $60$% of the track. If $A$ returns to $P$ at $10:12$ am, then $B$ returns to $P$ at

  1. $10:25$am
  2. $10:18$am
  3. $10:27$am
  4. $10:45$am
in Quantitative Aptitude 11.5k points 213 1338 2320
edited by
125 views

1 Answer

0 votes

Ans is option (C)

Let the diameter of the track be  $d$ mtr. Then the length of the track is  $\pi d$ mtr. Let the speeds of ant$_{1}$ and ant$_{2}$ be  $v_{1},v_{2}$ mtr/min  respectively.

Then, let in time  $t$ minutes,  ant$_{1}$ covers $60$% of the track i.e. distance of  $0.6\pi d$ mtr.

Then in the same time  $t$ minutes, ant$_{2}$  covers $40$%  of the track i.e. distance of  $0.4\pi d$ mtr.

For ant$_{1}$ we have following equations:   $t=\frac{0.6\pi d}{v_{1}}$  -----(1)    and     $t+12=\frac{\pi d}{v_{1}}$  ------(2)

Dividing (2) by (1), we get  $t=18$ minutes

For ant$_{2}$ we have following equations:   $t=\frac{0.4\pi d}{v_{2}}$  -----(3)    and     $t+y=\frac{\pi d}{v_{2}}$  ------(4)    (t+y is the complete time taken by ant$_{2}$ to complete the track) .

Dividing (4) by (3), we get  $y=27$ minutes

After t minutes , it is  $10:00$ A.M when the two ants meet for the first time. From there , it takes $27$ minutes for ant$_{2}$ to reach point P.

So,  ant$_{2}$  reaches point P at  $10:27$ A.M.

 

238 points 2 2 4

Related questions

0 votes
1 answer
1
171 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 $8$ $7$ $9$ $10$
asked Mar 20, 2020 in Quantitative Aptitude jothee 11.5k points 213 1338 2320 171 views
0 votes
1 answer
2
93 views
If x is a real number, then $\sqrt{\log _{e}\frac{4x-x^{2}}{3}}$ is a real number if and only if $1\leq x\leq 2$ $-3\leq x\leq 3$ $1\leq x\leq 3$ $-1\leq x\leq 3$
asked Mar 20, 2020 in Quantitative Aptitude jothee 11.5k points 213 1338 2320 93 views
0 votes
1 answer
3
219 views
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 $24$ $26$ $32$ $35$
asked Mar 20, 2020 in Quantitative Aptitude jothee 11.5k points 213 1338 2320 219 views
0 votes
0 answers
4
78 views
How many pairs $(m,n)$ of positive integers satisfy the equation $m^{2}+105=n^{2}$?____
asked Mar 20, 2020 in Quantitative Aptitude jothee 11.5k points 213 1338 2320 78 views
0 votes
0 answers
5
171 views
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? $14$ $13$ $15$ $12$
asked Mar 20, 2020 in Quantitative Aptitude jothee 11.5k points 213 1338 2320 171 views
...