Question

Q36. A plane left 30 minutes later than the scheduled time and in order to reach its destination 1500 kilometres away in time, it has to increase its speed by 250 kilometres/hour from its usual speed. Find its usual speed.

• A. (a) 1000 kilometres/hour
• B. (b) 750 kilometres/hour
• C. (c) 850 kilometres/hour
• D. (d) 650 kilometres/hour

Answer 1

The correct option is B

(b) 750 kilometres/hour

Let v be the speed

$\frac{1500}{v}-\frac{1500}{v+250}=\frac{1}{2}$

Verifying from the answer choices, v = 750 is the right choice.

Here follows an alternative method.

Power of the denominator in identifying the right answer:

If you understand the following technique you would at once identify the correct answer choice. The essence of the technique lies in recognizing the type of denominator that should be compatible with data of the problem. Here in this problem you are working with a given difference in time that arises because of a change in velocity in negotiating a distance. The distance is 1500 kilometres.

The difference in time $\frac{1}{2}hour$

The increase in velocity is 250 kilometres/hour

$Time=\frac{Distance}{Speed}$

Difference in time $\frac{1500}{Speed}-\frac{1500}{Speed+250}$

$\frac{1}{2}=\frac{1500}{Speed}-\frac{1500}{Speed+250}$

In the exam hall you do not need to write any of these because these are obvious.

Now take answer choice (a).

In (1) $\frac{1500}{Speed}=\frac{3}{2}$ is OK for this data

But = $\frac{1500}{1000+250}=\frac{6}{5}$ is not OK

because denominator 5 is not compatible with $\frac{1}{2}$ on the left hand side of (1).

Hence (a) can be rejected.

Try with (b) you would see that is a correct answer choice.

For practice let us would also work through answer choice (c)

$\frac{1500}{Speed}=\frac{1500}{850}=\frac{30}{17}$

Such a denominator like 17 is not compatible with $\frac{1}{2}$

Also, $\frac{1500}{850+250}=\frac{15}{11}$ is also not compatible. So without any calculation you can reject such answer choices