Now we can see that whatever the value of ‘a’, 126a + 133 will always give an integral value.
So, it now depends upon 11/a only
=> a can have any integral value, which is a factor of 11.
The integers, which will satisfy this condition are ±1, ±11. Thus, in total,a can take 4 values.
Let the numbers be x and y.
Then, xy = 39375 and x/y = 7.
(xyxy//)=39375/7
=>y2 =5625
=> y = 75
=> x = 7y = 7 x 75 = 525.
Sum of the numbers = 525 + 75 = 600.
In a mile race, Yuvraj can be given a start of 128 m by Virat. If Virat can give Rohit a start of 4 m in a 100 m dash, then who out of Yuvraj and Rohit will win a race of one and half miles, and what will be the final lead given by the winner to the loser? One mile is 1,600 m.
OPtion
1) Yuvraj, 10 m
2) Rohit, 10 m
3) Yuvraj, 25 m
4) Rohit, 25 m
5) Yuvraj, 50 m
6) Rohit, 50 m
7) Yuvraj, 80 m
8) Rohit, 80 m
9) Rohit, 100 m
10) None of these
Solution
In a mile race, Yuvraj can be given a start of 128 m by Virat. This means that Virat can afford to start after Yuvraj has traveled 128 m and still complete one mile with him. In other words, Virat can travel one mile, i.e. 1,600 m in the same time as Yuvraj can travel (1600 – 128) = 1,472 m. Hence, the ratio of the speeds of Virat and Yuvraj = Ratio of the distances traveled by them in the same time = 1600/1472 = 25 : 23.
Virat can give Rohit a start of 4 miles. This means that in the time Virat runs 100 m, Rohit only runs 96 m. So the ratio of the speeds of Virat and Rohit = 96 : 100 = 25 : 24.
Hence, we have B : A = 25 : 23 and B : C = 25 : 24. So A : B : C = 23 : 25 : 24. This means that in the time Rohit covers 24 m, Yuvraj only covers 23 m. In other words, Rohit is faster than Yuvraj. So if they race for 1.5 miles = 2,400 m, Rohit will complete the race first and by this time Yuvraj would only complete 2,300 m. In other words, Rohit would beat Yuvraj by 100 m