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Mr. Rawat wishes to cross a the Sahara desert.
It requires 6 days to cross.
One man can only carry enough food and water for 4 days.
What is the fewest number of other men required to help carry enough food for Mr. Rawat to cross ?
He need only few helpers in the case!
Source
What's the challenge?
Mr. Rawat should take 2 helpers - let's name them as A & B.
Let 1 be the unit of food & water that is required for 1 day. So all are going to carry 4 units of food & water.
On the day 1, Mr. Rawat, B & A himself take the food & water from A. Then A will left with only 1 unit & to survive he should go back. In 1 day, he can consume that 1 unit of food & water & travel back to the origin.
On the day 2, Mr. Rawat & B consume 2 units food & water of helper B. Now helper B has to move back to origin with 2 units of food & water in 2 days. Again he can easily go back in 2 days covering distance traveled by him in 2 days of forward journey.
Now Mr. Rawat has 4 units of food & water which he can use in his 4 day's journey of crossing Sahara desert.
Lavesh, Bolt, and Lewis race each other in a 100 meters race. All of them run at a constant speed throughout the race.
Lavesh beats Bolt by 20 meters.
Bolt beats Lewis by 20 meters.
How many meters does Lavesh beat Lewis by ?
Know here the answer!
Source
What was the question?
Let Lavesh's speed be 10 m/s. Then he must have taken 10 seconds to finish the race. Since Bolt was beaten by Lavesh by 20 m he must have run 80m when Lavesh finished race in 10 seconds (t=10). So his speed would be 8 m/s.
Now Bolt requires 100/0.8 = 12.5 seconds to finish the race. When he finished, Lewis was 20m behind i.e. 80m from starting point at t = 12.5. So Lewis speed is 80/12.5 = 6.4 m/s
At t = 10 seconds, when Lavesh finished his race Lewis must be at 6.4 x 10 = 64 m from starting point. Hence Lavesh beats Lewis by 100 - 64 = 36 m.
Another method.
Let L be the speed of Lavesh, B be the speed of Bolt & W be that of Lewis. Then,
L/B = 100/80 = 5/4
L = (5/4) B .......(1)
Similarly,
B/W = 100/80 = 5/4
B = (5/4) W .......(2)
Putting (2) into (1),
L = (5/4) x (5/4) W
L/W = 25/16
L = (25/16) W
For given time t, when Lavesh finished the race,
Distance by L/ Distance by W = 25 / 16
100 m/ Distance by W = 25 / 16
Distance by W = (16 x 100) / 25 = 64.
So when Lavesh finished cross line at 100 m, Lewis was at 64m i.e. 36m behind. In other words, Lavesh beats Lewis by 100 - 64 = 36 m.
