Bissoy.com
Doctors Medicines MCQs Q&A

Rakesh and Abhinay are swimmers and they participated in a swimming race in which they had to travel between two ports A and B and returned back from B to A. Rakesh took 37.5 seconds to complete the race and Abhinay took 200/3 seconds to complete the race. If the speed of Abhinay is increased by 100% then find the approximate difference between the time taken by Rakesh and Abhinay to complete the race where the speed of stream is 5m/s and the distance between two ports is 250m.

Rakesh and Abhinay are swimmers and they participated in a swimming race in which they had to travel between two ports A and B and returned back from B to A. Rakesh took 37.5 seconds to complete the race and Abhinay took 200/3 seconds to complete the race. If the speed of Abhinay is increased by 100% then find the approximate difference between the time taken by Rakesh and Abhinay to complete the race where the speed of stream is 5m/s and the distance between two ports is 250m. Correct Answer 10.84 seconds

Given:

Rakesh took 37.5 seconds to complete the race

And Abhinay took 200/3 seconds to complete the race

Formula used: Distance = Speed × Time, (s = v × t)

Calculation:

And let the speed of Rakesh be x m/s

And let the speed of Abhinay be y m/s

So, the speed of Rakesh in downstream = (x + 5) m/s

And the speed of Abhinay in downstream = (y + 5) m/s

So, speed of Rakesh in upstream  = (x – 5) m/s

And the speed of Abhinay in upstream = (y – 5) m/s

Now, according to question,

250/(x + 5) + 250/(x – 5) = 37.5

⇒ 1/(x + 5) + 1/(x – 5) = 3/20

⇒ 2x/(x2 – 25) = 3/20

⇒ 3x2 – 40x – 75 = 0

⇒ 3x2 – 45x + 5x – 75 = 0

⇒ 3x (x - 15) + 5 (x - 15) = 0

⇒ (x - 15) (3x + 5) = 0

So, x = 15

And also according to question,

250/(y + 5) + 250/(y – 5) = 200/3

⇒ 1/(y + 5) + 1/(y – 5) = 4/15

⇒ 2y/(y2 – 25) = 4/15

⇒ 4y2 – 30y – 100 = 0

⇒ 4y2 – 40y + 10y – 100 = 0

⇒ 4y (y – 10) + 10 (y – 10) = 0

⇒ (y – 10) (4y + 10) = 0

So, y = 10 (as 2nd value of y is negative and speed cannot be negative)

New speed of Abhinav = 10 × 200% = 20 m/s

So, the time taken by Abhinav to complete the race = 250/(20 + 5) + 250/(20 – 5) = 26.67 seconds.

∴ Required difference = 37.5 – 26 .67 =10.84 seconds.

Related Questions

The time taken by a ship to travel 1000 km upstream is 40 hours more than the time taken by it to travel the same distance in downstream. The speed of the ship in still water is 200% more than that of the speed of stream. Quantity I: How much time the ship will take to travel the same distance in upstream?  Quantity II: How much time the ship will take to travel 2000 km downstream if due to wind, the speed of stream was increased by 50%?
If the sum of the total time taken by boats X1 to travel D km each upstream and X2 to travel downstream is 4 hours and the sum of the total time taken by boats X1 to travel downstream and X2 to travel upstream the same distance D km each is 12 hours. Time taken by X2 to travel upstream exceeds its downstream time by t1 hours. Similarly, the time taken by X1 to travel upstream exceeds its downstream time by t2 hours. What is the value of (t1 - t2)?
In the following question, two statements are numbered as A and B. On solving these statements we get quantities A and B respectively. Solve for the both quantities and chose the correct option. Quantity A: The ratio of speed of boat to speed of stream is 2 : 1, If the boat travels 162 km and come back to starting point in 36 hour. What is the difference between the time taken by the boat to go upstream and the time taken by the boat to go downstream? Quantity B: The speed of the stream is 6 km/hr and the distance travelled by the boat is 60 km. If the boat covered half distance upstream with usual speed and other half with double its speed, then it takes 7.5 hours less time than usual time to go upstream. Find the total time taken by the boat to go upstream and downstream?
In the following question, two statements are numbered as A and B. On solving these statements, we get quantities A and B respectively. Solve both quantities and choose the correct option. Quantity A: Superman and Batman in their boat are moving towards each other If Superman travel against the stream and Batman along the stream they are at a distance of 2300 km from each other. If the Speed of Stream is 20 km/h and Speed of Superman’s Boat is 100 km/h and Speed of Batman’s Boat is 130 km/h. Find the Time Taken to meet each other Quantity B: Tony Stark is flying in his suit 1 hour before Captain America with the speed of 200 km/h. If Captain America is chasing him in the boat which runs at a speed of 270 km/h against a stream which has speed of 20 km/h. Find the time in which he catches the Tony Stark.
Questions below followed by two quantities. Find the relation between them. The table shows the distance travelled by five different boats upstream, the speed of the boat in still water and the time taken by them to cover the upstream distance. Boats Upstream distance Speed of boat Time taken  A  240 km  15 km/hr  20 hr  B  150 km  10 km/hr  25 hr  C  350 km  20 km/hr  50 hr  D  96 km  8 km/hr  16 hr  E  126 km  26 km/hr  9 hr   Quantity I: Boat B travel 238 km distance downstream in certain time. How much downstream distance boat D will cover at the same time? Quantity II: Boat E travel 722 km distance downstream in certain time. How much downstream distance boat A will cover at the same time?
What is the distance covered by boat N upstream in 5 hours? Which of the following option is sufficient alone to find the answer? A) Boat M is travelling downstream with 20% more downstream speed of boat N. Speed of boat M in still water is 10% more than the speed of boat N in still water. B) Boat M and Boat N are travelling downstream with speed 33 km/hr and 40 km/hr respectively and speed of boat M is still water is 2 times the speed of stream. C) Speed of boat M in still water is 6 km/hr less then speed of boat N in still water and speed of stream is 10 km/hr. D) Speed of stream is ½ times the speed of boat N in still water and downstream speed of boat M is 44 km/hr. E) Speed of stream is 10 km/hr and ratio of upstream speed of boat M and boat N is 3 : 2 respectively.
In a survey of 25 students, it was found that 15 had taken Mathematics, 12 had taken Physics and 11 had taken Chemistry, 5 had taken Mathematics and Chemistry, 9 had taken Mathematics and Physics, 4 had taken Physics and Chemistry and 3 had taken all the three subjects. Find the number of students who had taken both Physics and Chemistry but not Mathematics.
The following question, there are three statements I, II and III. Read the question carefully and mark your answer according to which statements(s) is/are sufficient to the answer the question. What is the Speed of the stream? Statement I: The distance between two points A and B is a km and the boat cover 90km along the stream in 5 hours. Statement II: The distance travelled along the stream is four times the total distance and that against the stream is three times the total distance Statement III: The total time taken against the stream is 10% more than that along the stream
In a survey of university students, 64 had taken Drama course, 94 had taken Dance course, 58 had taken a Singing course, 28 had taken Drama and singing course, 26 had taken Drama and dance course, 22 had taken Dance and singing course, and 14 had taken all the three courses. Find how many have taken only one course?
The five addresses are given below. Which two addresses are exactly the same? 1. Mr. K. Raghuramiaya, K-379, Guntakalpkam, Fortbridge Street, Telampuram - 375 612 2.Mr. K. Raghuramaiya, K-379, Guntakalpkam, Fortbridge Street, Telampuram - 375 612 3.Mr. K. Raghuramiaya, K-379, Guntaklapkam, Fortbridge Street, Talempuram - 375 612 4.Mr. K. Raghuramaiya, K-379, Guntakalpkam, Fortbridge Street, Telampuram - 375 612 5. Mr. K. Raghuramaiya, K-379, Guntakalpakam, Fortbridge Street, Talempuram - 375 612