Puzzle_7

1. 40 cows graze a pasture in 40 days,30 cows graze the same pasture in 60 days.how many days does 20 cows take to graze it.

Ans: 120 days.
Let 'x' be the amount of grazed by a cow per day,
Let 'y' be the growth rate of grass per day,
Let 'z' be the amount of grass present initially,
So, 40 cows can graze (40*x) amount of grass per day and (40*x*40) amount of grass for 40 days.
For 40 days, the growth of grass is (40*y)
So, (40*x*40) = (z + 40*y)
For 30 cows it takes 60 days, so,
(30*x*60) = (z + 60*y) so,
1600x - 40y - z = 0 ----- 1
1800x - 60y - z = 0 ----- 2
Subtracting we get, 10x = y ,
Sub. 10x=y in 1 or 2,
we get z = 120y or z = 1200x
For, 20 cows,
20*x*N = z + N*y
Sub, 10x=y and (z=120y or 1200x), we get N = 120
Therefore, for 20 cows it takes 120 days to graze.

2. A person from washington came to india.One evening at 6.00 p m he started walking at the speed of 40 km/hr andclimbed the slope at speed of 30 km/hr.From there he walked back to the source at the same speed at 9.00 p m.what is the distance he covered in one way.

Answer: 105 km
read the question carefully...
he starts his return journey at 9:00pm..
so one way journey time is 3hrs
So the eqn becomes
avg spd =35kmph
(x+y)/35=3
x+y=35*3 =105