Question:
The reduction in speed of a railway engine is directly proportional to the square root of the number of compartments attached to it. With no compartments attached to the engine, the speed is 42 km/h. With 9 compartments attached to the engine, the speed is 24 km/h. What are the maximum number of compartments that can be attached to the engine?
The reduction in speed of a railway engine is directly proportional to the square root of the number of compartments attached to it. With no compartments attached to the engine, the speed is 42 km/h. With 9 compartments attached to the engine, the speed is 24 km/h. What are the maximum number of compartments that can be attached to the engine?
Show Hint
When dealing with proportional relationships, be sure to apply the square root function correctly and solve for unknowns.
Updated On: Aug 5, 2025
- 49
- 48
- 46
- 47
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Let \( k \) be the constant of proportionality, and let the speed when there are \( n \) compartments attached be \( v \). From the relation, we have:
\[
v = 42 - k\sqrt{n}
\]
Using the given values:
\[
24 = 42 - k\sqrt{9} \quad \Rightarrow \quad k = \frac{18}{3} = 6
\]
Now, substituting \( k = 6 \) into the equation for \( v = 0 \), we get the maximum number of compartments as 48.
Was this answer helpful?
0
0
Top CAT Quantitative Aptitude Questions
- In a triangle ABC,AB=AC=8cm. A circle drawn with BC as diameter passes through A. Another circle drawn with center at A passes through B and C. Then the area,in sq.cm,of the overlapping region between the two circles is
- The simple interest accrued on an amount of Rs.25,000 at the end of three years is Rs.7,500. What would be the compound interest accrued on the same amount at the same rate in the same period?
- What is the sum of all roots of the equation \(|x+4|^2–10|x+4|=24\)?
- A solid metal sphere is melted and smaller spheres of equal radii are formed. 10% of the volume of the sphere is lost in the process. The smaller spheres have a radius which is \(\frac{1}{9}\text{th}\) the larger sphere. If 10 litres of paint were needed to paint the larger sphere,how many litres are needed to paint all the smaller spheres?
- The ratio of the ages of a husband and his wife when they got married was 6:5. 4 years and 6 years after their marriage they had their 1st and 2nd children. The sum of the present ages of the husband and wife is 6.4 times the sum of the present ages of their children. The average age of the family at present is 18.5 years. Find the ratio of the ages of the husband and wife when their second child was born.
View More Questions
Top CAT Time, Speed and Distance Questions
- Brishti went on a 8-hour trip in a car, before the trip the car had traveled a total of x kms till then, where x is a whole number and is palindromic, At the end of his trip the car had had traveled a total of 26862 km. If Bristi never drove at more than 110 km/h, then the greatest possible average speed at which see dove is?
- Two cars travel the same distance starting at 10:00 am and 11:00 am, respectively, on the same day. They reach their common destination at the same point of time. If the first car travelled for at least 6 hours, then the highest possible value of the percentage by which the speed of the second car could exceed that of the first car is
- In a race of three horses, the first beat the second by 11 metres and the third by 90 metres. If the second beat the third by 80 metres, what was the length, in metres, of the racecourse?
- One can use three different transports which move at 10, 20, and 30 kmph, respectively. To reach from A to B, Amal took each mode of transport 1/3 of his total journey time, while Bimal took each mode of transport 1/3 of the total distance. The percentage by which Bimal’s travel time exceeds Amal’s travel time is nearest to
- The wheels of bicycles A and B have radii 30 cm and 40 cm, respectively. While traveling a certain distance, each wheel of A required 5000 more revolutions than each wheel of B. If bicycle B traveled this distance in 45 minutes, then its speed, in km per hour, was
View More Questions
Top CAT Questions
- Compare and contrast between Portia and Jessica characters in Merchant of Venice.
- In a triangle ABC,AB=AC=8cm. A circle drawn with BC as diameter passes through A. Another circle drawn with center at A passes through B and C. Then the area,in sq.cm,of the overlapping region between the two circles is
- The simple interest accrued on an amount of Rs.25,000 at the end of three years is Rs.7,500. What would be the compound interest accrued on the same amount at the same rate in the same period?
- What is the sum of all roots of the equation \(|x+4|^2–10|x+4|=24\)?
- A solid metal sphere is melted and smaller spheres of equal radii are formed. 10% of the volume of the sphere is lost in the process. The smaller spheres have a radius which is \(\frac{1}{9}\text{th}\) the larger sphere. If 10 litres of paint were needed to paint the larger sphere,how many litres are needed to paint all the smaller spheres?
View More Questions