Find the total no.of rats in the first portion and the no.of rats the cat cought.
Asked by | 19th Jun, 2009, 09:01: PM
Let w, x, y, z be the number of rats in the first, second, third and fourth section respectively.
And the cat catches A number of rats at a time.
So after she catches A number of rats in first section, the remaining rats i.e. w - A go to second section and the number of rats there doubles.
Hence, x + w - A = 2x.
After catching the same number of rats in second section, the remaining rats i.e. 2x - A go to third section, and the number of rats there triples.
Hence, y + 2x - A = 3y.
Similarly for fourth section,
z + 3y - A = 4z.
and finally the remaining rats i.e. 4z - A go to first section and cat catches A rats, there we exhaust of rats.
Hence, 4z - A - A = 0.
So rearranging the four equations,
w - x = A
2x - 2y = A
3y - 3z = A
2z = A,
So we have FIVE VARIABLES AND FOUR EQUATIONS.
we can express w, x, y, z in terms of A,
(substitute the expression of z in third equation to obtain y, then the expression for y in second and so on.)
z = A/2, y = 5A/6, x = 4A/3, w = 7A/3.
Let's PICK MINIMUM A i.e. NUMBER OF RATS THE CAT CATCHES AT A TIME AS 6,
then w = 14, x = 8, y = 5 and z = 3.
So TOTAL NUMBER OF RATS IN THE FIRST PORTION i.e. w = 14, and
TOTAL NUMBER OF RATS THE CAT CAUGHT = 6 X 5 = 30
Answered by | 19th Aug, 2009, 07:59: PM
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