### Discussion :: Arithmetic Reasoning - Section 1 (Q.No.25)

25. | If 100 cats kill 100 mice in 100 days, then 4 cats would kill 4 mice in how many days ? |
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Answer: Option D Explanation: |

Bala said: (Dec 21, 2011) | |

Is any other method available for this problem? Please explain. |

Priya said: (Aug 5, 2013) | |

1 cat kill 1 mice in 100 days. 4 cats kill 4 mice in 100 days. |

Aditya said: (Oct 9, 2013) | |

This means, Cats reduced from 100 to 4 so days increase. Mice reduced from 100 to 4 so days decrease. So actions get canceled out. Thus, days remain 100. |

Atharv said: (Sep 1, 2015) | |

I can't understand. |

San said: (Dec 18, 2015) | |

Please give me detailed explanation. |

Nicholas said: (Mar 22, 2016) | |

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. |

Gautham said: (Apr 19, 2016) | |

Actually, what do you mean? |

Suresh Raju said: (Jun 10, 2016) | |

100 cats can kill 100 mice in 100 days. That is 1 cat kills 1 mice in 100 days. Then if 4 cats have to kill 4 mice the time should not change. That is a cat can kill a mice in 100 days. 4 cats can kill 4 mice in 100 days. |

Shweta Koshija said: (Jul 23, 2016) | |

100 cats kill 100 mice in = 100 days. 1 cat kills 100 mice in = 100x100 days (since 1 cat has to do what 100 cats together did). 1 cat kills 1 mouse in = (100X100) / 100 = 100. So 4 cats kill 4 mice in 100 days (each cat will kill 1 mouse in 100 days). |

Candy said: (Sep 6, 2016) | |

Hi all, why it can't be like 1 cat is killing a mouse on the first day 2nd cat on the second day and so on? |

Parvesh said: (Sep 8, 2016) | |

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. |

Sarabjit said: (Oct 21, 2016) | |

@Parvesh. Your solution is more accurate and logical. |

Thanvi said: (Jan 19, 2017) | |

How can it be 100 days? Please explain in detail. |

Megha said: (Feb 25, 2017) | |

Didn't understand. Please explain for me. |

Abhinay said: (May 20, 2017) | |

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. |

Aastha said: (Sep 16, 2017) | |

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. |

Neha Singh said: (Sep 17, 2017) | |

It's best & easy explanation. Thanks. |

Shashi said: (Dec 3, 2017) | |

Nice explanation, I understand it @Aastha. |

Vanshika said: (Mar 10, 2018) | |

I can't understand it, please anyone help me. |

Shagandeep Randhawa said: (May 8, 2018) | |

There's a formula for this: No. of persons * No.of days/ work done. In first case = no. of persons* no. of days/work done in 2nd case. By calculating this method we will get the answer. |

Mridusmita said: (May 12, 2018) | |

Best Explanation @Aastha. |

Kamal said: (May 17, 2018) | |

@Aastha. Your method is quite easy to understand. Thanks. |

Yash said: (Jun 25, 2018) | |

@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. |

Unknown said: (Mar 11, 2020) | |

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. |

Eepp said: (May 26, 2020) | |

I am not getting the answer clearly. Someone, please explain the answer with a proper method. |

Bunu Rai said: (Oct 16, 2020) | |

Thanks for giving the explanation @Aastha. |

Vijju said: (Jan 13, 2021) | |

Please, explain clearly to understand. |

Pavithra said: (Jul 12, 2021) | |

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. |

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