The greatest number of wagons that can be attached to a locomotive engine if the speed is not to fall below 14 km. per hour is given as 144.

Which one of the following is correct in respect of the Question and the Statements given below?

Statement 1: The locomotive engine without any wagon can go at a rate of 50 km per hour.

Statement 2: The speed of the locomotive diminishes by a quantity which varies as the square root of the number of wagons attached.

Statement 3: With 16 wagons its speed is 38 km. per hour.

Correct option is A

Solution:

From Statement 2:

Speed decreases as square root of number of wagons.
Let the number of wagons be n.
Then speed
v = a − b × √n, where:

a = speed without wagons
b = a constant

Now we’ll use the statements to check if we can solve for n when v = 14

Statement 1:
The locomotive engine without any wagon can go at 50 km/h.
So when n = 0, v = 50
Substitute into the equation:
50 = a − b × √0
=> a = 50

This gives us a = 50

Statement 2:
Speed diminishes as square root of number of wagons
=> Confirms the form of the equation:
v = a − b × √n

This tells us the type of relationship

Statement 3:
With 16 wagons, speed = 38 km/h
Substitute into the equation:
v = 50 − b × √16
=> 38 = 50 − 4b
=> b = 3

Now we have both a = 50 and b = 3

Now compute the max n such that:
v = 50 − 3 × √n ≥ 14

Start solving:

50 − 3 × √n ≥ 14
=> 3 × √n ≤ 36
=> √n ≤ 12
=> n ≤ 144

So, max n = 144, which matches the given value

Which Statements Are Sufficient?
Statement 1 gives us a = 50

Statement 2 gives the functional form (square root relationship)

Statement 3 lets us calculate b = 3

Together, they let us compute max n = 144 accurately.

Final Answer:
S. Ans. (a) All the three statements together are sufficient.