Verbal Reasoning - Arithmetic Reasoning - Discussion

Cats : Mice : Days : : Cats : Mice : Days.
100 : 100 : 100 : : 4 : 4 : x
100/100 :100 : : 4/4 : x.
1:100 : : 1 : x.
1/100 : : 1/x.
x=(100*1)/1.

Therefore, x= 100.

The formula based on chain rule for time and work is:

No.of person(p1)*no of hours(h1)*no of days(d1)/No.of person(p2)*no of hours(h2)*no of days(d2)=w1/w2.

So by this if we put the respective values:

100(cat)*100(days)/4(mice)*x(days)=100(killed cats)/4(killed mice),

By cross multiplying:
100 * 100 * 4 = 100 * 4 * x.
Thus,
X = 100 days.

Please, explain clearly to understand.

Thanks for giving the explanation @Aastha.

100 cat's went for hunting mice in a day.
All 100 cats are able to catch only 1 mice per day.
Likewise, it took 100 days to catch 100 mice's.

Now we need to know for catching 4 mice's by 4 cat's how many days we want.
ANS.

1mice/100cats =0.01 mice per day per cat
0.01 mice per day *100 cats per day = 1 mice per day.
1 mice per day * 100 mice's = 100 days to catch 100 mice's

Likewise,

For catching 4mices by 4 cat's will be as follows.
0.01 mice by 1 cat *4 cat's per day= 0.04 mice per day.
1mice/0.04 mice per day = 25 days will take for 4 cat's to catch 1 mice.
Therefore 25 days per mice * 4 mice's =100 days.

i.e 100 days will be required for 4 cat's to catch 4 mice's.

@All.

I would rather say that 1 days should be the answer as if you go logically since the question doesn't indicate how 100 cats kills 100 mice in 100 days!

If there are 100 cats then they could also kills 100 mice in one day if ONE cat is killing ONE mice each day or all together all Cats Kills all the Mice in ONE SINGLE DAY.

There is lack of clarity in the question so the benefit of doubt says;.

4 CATS CAN KILL 4 MICE IN SINGLE DAY.

Hence, proved.

If it takes 100 days for one hundred cats to kill 100 mice, then one cat is killing one mouse in that 100 days.

Rather, if 100 cats kill 100 mice, then each cat is only killing one mouse. If this takes 100 days, then that's how long it takes for one cat to kill one mouse.

An equation to solve this or other question where work is doubled or halved.

(number of persons x number of days) /work done i.e. mice killed = (number of persons x number of days)/work done.

In this case (100 x 100)/100 = (4 x number of days(n))/4.

Solving this you get number of days n = 100.

If suppose M represents men/cats, D represents days, H represents hours and W represents work then,

(MxDxH)/W = CONSTANT.

In this question,
M = cats , D= days , W = Mice, then
(100 x 100)/100 = (4 x D)/4,
Solving this you will get,
D= 100 i.e. Answer.

Here we use the formula m1d1/w1 = m2d2/w2.