Can someone explain this very common type of Mensa question to me...?

Question

Ten people can paint 60 houses in 120 days, so 5 people can paint 30 houses in:

(a) 15

(b) 30

(c) 60

(d) 120.

The funny thing is I have a maths degree but can never get my head around this type of problem.

Answer 1

Half of the original question same answer.

Answer 2

I got this wrong until I read some answers.  Reminds of, if it takes one sheet 2 hours to dry on a windy day, how long will it take 6 sheets to dry on the same day?  It still takes two hours....

Answer 3

(D) 120

120 = 60/10 which is also 30/5

Answer 4

120 days - they still work at the same speed, but just half the people doing half the houses!

Answer 5

Half the people and half the houses

i.e

5 people 60 houses in 240days

therefore

5 people 30 houses in 120days!

Answer 6

Since you are a mathematician then you should approach it in a disciplined manner - although as everybody else has pointed out it is a simple problem since the numbers  have been made easy.

1. Calculate the number of 'man-days' (hey look it could be 'woman-days if you like) to paint a house.

10 people 120 days = 1,200 man-days

60 houses in 1,200 man-days implies 20 man-days per house.

2. Calculate the number of houses required to be painted by one man.

30 houses by five people so each 'man' needs  to do 6 houses.

3. Combine 1 and 2 therefore the answer is...

6 houses per man x 20 man days for each = 120.

Answer 7

120 days.   half the people will paint half as fast, so will only paint half as many houses.

Answer 8

(d) 120.

Answer 9

60 i think even though evrybody has written 120. coz if u see it logically and practically it should be 60.

Answer 10

i would say 60 days because you half everything along the you have 10 people vs 5 people 60 houses vs 30 houses so in my logic is it should take 60 days

So am I right

Answer 11

120 days

Lots of ways to explain it. One is half as many people half as many houses so same time.

Another way is 10 paint 60 in 120 days so 1 paints 6 in 120 days so 5 paint 5 times as many in 120 days i.e. 30 houses in 120 days.

The problem to any mathematically minded person is that the question is in fact nonsensical as there are more than mathematical factors in play in the real world.

It is almost as stupid as saying 10 people can push a bus 200 metres in 5 minutes, how long will it take 1 person to push a bus 200 metres?

Answer 12

UHHHHHH

                                               B