Three boys are racing around a circular
track each at a constant speed. Dinesh is
the fastest and passes Satish every 20
minutes. On the other hand Satish
passes Arun every 30 minutes. How often
does Dinesh pass Arun?
● 15 minutes
● 8 minutes
● 10 minutes
● 12 minutes
Answers
Given,
Three boys are racing around a circular
track each at a constant speed.
Dinesh is the fastest and passes Satish every 20 minutes.
Satish passes Arun every 30 minutes.
To find,
Total time in which Dinesh passes Arun.
Solution,
We can simply solve this mathematical problem using the following process:
Let us assume that,
The constant speed of Dinesh is x units.
The constant speed of Satish is y units.
The constant speed of Arun is z units.
The fixed circumference of the circular track = total distance covered in each complete round = R units = constant for all 3 riders
Mathematically,
Speed (s) = distance traveled (d)/time taken (t)
Distance covered by Satish in 20 minutes
= speed × time taken
= (20y) units
Now, according to the question;
Dinesh passes Satish in every 20 minutes
=> Distance covered by Dinesh in 20 minutes = (distance covered in 1 complete round) + (distance covered by Satish in 20 minutes) = (R + 20y) units
Now, according to the question;
(R + 20y)/20 = x
=> R = 20x - 20y => (x-y) = R/20 {Equation-1}
Now,
Distance covered by Arun in 30 minutes
= speed × time taken
= (30z) units
Now, according to the question;
Satish passes Arun every 30 minutes
=> Distance covered by Satish in 30 minutes = (distance covered in 1 complete round) + (distance covered by Arun in 20 minutes) = (R + 30z) units
Now, according to the question;
(R + 30z)/30 = y
=> R = 30y - 30z => (y-z) = R/30 {Equation-2}
Now, on adding equations 1 and 2, we get;
(x-y) + (y-z) = R/30 + R/20
=> (x-z) = 2R/60 + 3R/60 = 5R/60 = R/12
=> (x-z) = R/12
=> relative speed of Dinesh with respect to Arun = R/12 = distance covered per unit time
=> Dinesh passes Arun in every 12 minutes
Hence, Dinesh passes Arun every 12 minutes. (4th option)
Answer:
Given,
Three boys are racing around a circular
track each at a constant speed.
Dinesh is the fastest and passes Satish every 20 minutes.
Satish passes Arun every 30 minutes.
To find,
Total time in which Dinesh passes Arun.
Solution,
We can simply solve this mathematical problem using the following process:
Let us assume that,
The constant speed of Dinesh is x units.
The constant speed of Satish is y units.
The constant speed of Arun is z units.
The fixed circumference of the circular track = total distance covered in each complete round = R units = constant for all 3 riders
Mathematically,
Speed (s) = distance traveled (d)/time taken (t)
Distance covered by Satish in 20 minutes
= speed × time taken
= (20y) units
Now, according to the question;
Dinesh passes Satish in every 20 minutes
=> Distance covered by Dinesh in 20 minutes = (distance covered in 1 complete round) + (distance covered by Satish in 20 minutes) = (R + 20y) units
Now, according to the question;
(R + 20y)/20 = x
=> R = 20x - 20y => (x-y) = R/20 {Equation-1}
Now,
Distance covered by Arun in 30 minutes
= speed × time taken
= (30z) units
Now, according to the question;
Satish passes Arun every 30 minutes
=> Distance covered by Satish in 30 minutes = (distance covered in 1 complete round) + (distance covered by Arun in 20 minutes) = (R + 30z) units
Now, according to the question;
(R + 30z)/30 = y
=> R = 30y - 30z => (y-z) = R/30 {Equation-2}
Now, on adding equations 1 and 2, we get;
(x-y) + (y-z) = R/30 + R/20
=> (x-z) = 2R/60 + 3R/60 = 5R/60 = R/12
=> (x-z) = R/12
=> relative speed of Dinesh with respect to Arun = R/12 = distance covered per unit time
=> Dinesh passes Arun in every 12 minutes
Hence, Dinesh passes Arun every 12 minutes. (4th option)