Hi Maihuna,
you want to know the best approach, but you have not posted the five answer choices. Why haven't you? What if the fastest approach involved making use of the answer choices? Understand that great test-takers employ alternative approaches such as using the answer choices or backsolving from the answer choices. In fact, the test-maker is always looking to reward non-traditional approaches. In a fuzzy word-rate problem such as this one, backsolving is a good candidate for being the most efficient way of solving. Remember, it is a multiple choice exam--that means a) you don't have to show any work so don't adopt a long-winded algebraic approach if you don't have to and b) the correct answer is there, somewhere in the five answer choices--we can use this!
The wording of this question is very ambiguous. Among other glaring problems, the question should have stipulated that everyone's speed was constant.
Here is what I think the question meant. They all depart from point A at the same time. But Ram is driving a motorbike towards point B carrying Mohan while Shyam starts walking towards point B. At some point in the journey, prior to arriving at point B, Ram drops Mohan off. Because the motorbike was presumably traveling faster than Shyam's walking speed, Ram and Mohan have gained on Shyam. So, when Ram drops Mohan off, Mohan continues walking towards point B while Ram reverses direction, retrieves the trailing Shyam, and then turns back and continues heading towards point B carrying Shyam on the bike. Ram and Shyam arrive at point B at the same time that Mohan does. And we know that the distance separating point A from point B is 60 km while Shyam and Mohan's (constant) walking speed is 5 km/hr. The question is asking how much time has elapsed between their (simultaneous) departure from point A and their (simultaneous) arrival at point B.
Now, if this is the question, there are an infinite number of solutions, and there is no correct answer. There are only three ways there can be a correct answer here: a) if the question stem said "which of the following COULD be the time"; b) if one of the answer choices stated "It cannot be determined from the information given"; or c) if the answer choices were ranges.
There are different ways of proving that there are an infinite number of solutions here. First of all, we don't have any information about the motorbike's speed; the only thing we know is that it must be faster than 5km/hr. If the motorbike's speed was 5.00000....1 km/hr, then the total time would be very close to (but just a tad under) 12 hours. On the other hand, what if the motorbike's speed was very fast, say, close to infinity, or even, say, infinity. If the motorbike's speed was infinite, then Ram would, in a single instant, carry Mohan from A to B, return to A and then carry Shyam from A to B. Then, the time of travel would be zero. Therefore, the only thing we know for sure about the time is that it is between zero and some number just under 12.
Another way of proving that there are an infinite number of solutions is to set-up equations. No matter what algebraic approach you take, you will always have one fewer equations than you do have variables.
I would not trust questions from this source.
Kaplan Teacher in Toronto
