# CAT2019-2: 76

0 votes
158 views
John jogs on track A at $6$ kmph and Mary jogs on track $B$ at $7.5$ kmph. The total length of tracks $A$ and $B$ is $325$ metres. While John makes $9$ rounds of track $A$, Mary makes $5$ rounds of track $B$. In how many seconds will Mary make one round of track $A$?______

edited

## 1 Answer

0 votes

Ans is (48)

Let the lengths of tracks A and B be $x,y$ respectively.

Speed of John and Mary in m/s : $\frac{5}{3},\frac{25}{12}$  (by multiplying speed in km/h by  $\frac{5}{18}$ )

Given  $x+y=325$  and  $\frac{9x}{\frac{5}{3}}=\frac{5y}{\frac{25}{12}}$

Solving these two equations ,we get  $x=100mtr$

$\therefore$ Time taken by Mary to complete track A :   $\frac{100mtr}{\frac{25}{12}m/s}=48$  seconds

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 $8$ $7$ $9$ $10$
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 $1\leq x\leq 2$ $-3\leq x\leq 3$ $1\leq x\leq 3$ $-1\leq x\leq 3$
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 $24$ $26$ $32$ $35$
0 votes
0 answers
4
78 views
How many pairs $(m,n)$ of positive integers satisfy the equation $m^{2}+105=n^{2}$?____
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? $14$ $13$ $15$ $12$