Question

The ratio of the speeds of Amar, Akbar and Antony is 8: 5: 4. Akbar takes 15 minutes more than Amar to cover a certain distance, find the time taken by Antony to cover the same distance.
A. 30 minutes
B. 60 minutes
C. 40 minutes
D. 50 minutes

Answer 1

Hint: At first, consider the speed of Amar, Akbar and Antony as 8u, 5u and 4u and distance covered by them as D. Then, use the formula,
\[Time{\rm{ = }}\dfrac{{Dis\tan ce}}{{Speed}}\]
After this, use the given condition to find distance in terms of u and thus, find time taken by Antony.

Complete step-by-step answer:
In the question, we are given the speeds of Amar, Akbar and Antony which is 8: 5: 4. Now, it is further said that, time taken to cover a distance by Akbar is 15 more minutes than Amar and from this, we have to find the time taken by Antony to cover the same distance.
Let's suppose the speed of Amar, Akbar and Antony is 8u, 5u and 4u respectively and the distance covered by them is D.
Now, here we will use the formula, \[{\rm{Speed = }}\dfrac{{{\rm{Distance}}}}{{Time}} \Rightarrow Time{\rm{ = }}\dfrac{{Dis\tan ce}}{{Speed}}\]
Thus, from the given formula, we can say that, the time taken by each of them is:
Time taken by Amar\[ = \dfrac{D}{{8u}}\]
Time taken by Akbar\[ = \dfrac{D}{{5u}}\]
Time taken by Antony\[ = \dfrac{D}{{4u}}\]
We are told that the time taken by Akbar is 15 more than that of Amar. So, we can express it in form of equations,
\[\dfrac{D}{{5u}} - \dfrac{D}{{8u}} = 15\]
Now, taking \[LCM\] we get,
\[\dfrac{{8D - 5D}}{{40u}} = 15\]
Which can be simplified as,
\[\dfrac{{3D}}{{40u}} = 15\]
Now, we will do cross multiplication, so we get,
\[3D = 600u\]
Hence, the value of D is 200u.
Now, as we know, time taken by Antony to cover a distance D is \[\dfrac{D}{{4u}}\]. So, as we know that the value of D is 200u. So, we can find the time taken by him which is \[\dfrac{{200u}}{{4u}} \Rightarrow 50{\rm{ minutes}}{\rm{.}}\]
Hence, the correct option is D.

Note: Students while dealing with speed and distance questions, must know the basic formula such as the relation between speed, distance and time which comes handy most of the time. The formula is \[Time{\rm{ = }}\dfrac{{Dis\tan ce}}{{Speed}}\]. In this type of questions, always one of the factors will be constant, i.e. here the distance was the same, so we took it as a constant, D. Similarly if time or speed were given to be the same, we would have taken them as constants, say T and S.