Two bike riders ride in opposite directions around a circular track, starting at the same time from the same point. Biker A rides at a speed of 16 kmph and biker B rides at a speed of 14 kmph. If the track has a diameter of 40 km, after how much time (in hours) will the two bikers meet?

Correct Answer: 11

Explanation:

Do not assume that AB and C are on a straight line. Make a diagram with A and B marked 5 miles apart. Draw a circle centered on B, with radius 6. C could be anywhere on this circle. The minimum distance will be 1, and maximum 11

Correct Answer: 4 kms

Explanation:

Let the actual distance be t kms

Now, According to the data,

 

$$\begin{gathered} 5 t + 8 60 = 6 t \\ = > 5 60 t + 8 60 = 6 t \\ = > 60 t + 8 = 72 t \\ = > 8 = 12 t \\ = > t = 8 / 12 = 2 / 3 hrs \end{gathered}$$

 

Now, the total distance = 6t = 6 x 2/3 = 2 x 2 = 4 kms.

Correct Answer: 20 km

Explanation:

Average speed = 2 a b a + b, here a=25 b=4
= 2 x 25 x 4/(25+4) = 200/29 km/hr.

Distance covered in 5 hours 48 minutes
= Speed x time = (200/29)x (29/5) Distance covered in 5 hours 48 minutes = 40kms.

Distance of the post office from the village = (40/2) = 20 km.

Correct Answer: 55 kms

Explanation:

Let x and y be the respective km's travelled by man via taxi and by his own car.
Given x + y = 90 => x = 90 - y
But according to the question,
7x + 6y = 595
7(90-y) + 6y = 595
=> 630 - 7y + 6y = 595
=> y = 630 - 595 = 35
=> x = 90 - 35 = 55
Therefore, the distance travelled by taxi is 55 kms.

Correct Answer: 3h

Explanation:

Time ( when X was 30 km ahead of Y) = (120-30)/20 =4.5h

Time ( when Y was 30 km ahead of X) = (120+30)/20 = 7.5 h

Thus, required  difference in time = 3h

Correct Answer: 70 kms

Explanation:

Let the time taken by train be 't' hrs.

Then,

40 t = 35 t + 15 60

40t = 35t + 35/4

t = 7/4 hrs

Therefore, Required length of the total journey d = s x t

= 40 x 7/4

= 70 kms.

Correct Answer: 1400

Explanation:

Given the ratio of the circumference of front wheel  is 40 inches and back wheel is 70 inches. 

 

Distance covered = Circumference of the wheel × No. of Revolutions made by the wheel

 

If n is the number of revolutions made by back wheel, the number of revolutions made by front wheel is n+15

 

Distance covered by both the wheels is the same

 

i.e, 40*(n+15)=70n

 

 n=20 

 

 

 

                Front wheel      :      Back Wheel 

 

 Circumference       40      :      70 

 

 Revolutions           35      :      20

 

 

 

Distance covered  :  40×35 = 70×20 = 1400 inches.

Correct Answer: 48 kmph

Explanation:

Let the initial speed of Akhil be '4p' kmph

Then speed after decrease in speed = '3p' kmph

We know that, 

Change in speed == Change in time

According to the given data,

$$\begin{gathered} 24 3 p - 24 4 p = 35 - 25 60 \\ = > p = 12 \end{gathered}$$

 

Hence, the initial speed of Akhil = 4p = 4 x 12 = 48 kmph.

Correct Answer: None of these

Explanation:

Let t be the time after Kajol starts, when she meets Ajay, then 

               t = 300/(x+y) 

 This should be less than 2.5 or (x+y)>120 

Since       y= 3x/2  =>  y > 72

This (y>72) is greater than 67.5 km/h and hence Shahrukh will always overtake Ajay before he meets Kajol.

Correct Answer: 27 sec

Explanation:

Time taken to meet for the first time anywhere on the track

= length of the track / relative speed

= 300 / (15 + 25)5/18 = 300x 18 / 40 x 5 = 27 seconds.