Brain Teaser #002:
A contractor had employed 100 laborers for a flyover construction task. He did not allow any woman to work without her husband. Also, at least half the men working came with their wives.
He paid five rupees per day to each man, four rupees to each woman and one rupee to each child. He gave out 200 rupees every evening.
How many men, women and children were working with the constructor?
Answer to Brain Teaser #001:
The last person covered 120.71 meters.
It is given that the platoon and the last person moved with uniform speed. Also, they both moved for the identical amount of time. Hence, the ratio of the distance they covered - while person moving forward and backward - are equal.
Let's assume that when the last person reached the first person, the platoon moved X meters forward.
Thus, while moving forward the last person moved (50+X) meters whereas the platoon moved X meters.
Similarly, while moving back the last person moved [50-(50-X)] X meters whereas the platoon moved (50-X) meters.
Now, as the ratios are equal,
(50+X)/X = X/(50-X)
(50+X)*(50-X) = X*X
Solving, X=35.355 meters
Thus, total distance covered by the last person
= (50+X) + X
= 2*X + 50
= 2*(35.355) + 50
= 120.71 meters
Note that at first glance, one might think that the total distance covered by the last person is 100 meters, as he ran the total length of the platoon (50 meters) twice. TRUE, but that's the relative distance covered by the last person i.e. assuming that the platoon is stationary.
(Answer to today's brain teaser to be published tomorrow at 10 am)
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