# Ratio , proportion question

It will take 24 men working 9 hours a day each of build a house in 45 days . Given that all men work at the same rate,

(A) how many days will 18 men take to build the same house if they work 8 hours a day?

(B) how many hours per day must 20 men work if the house is to be completed in 48 days?

I'm having my mid-year examinations tomorrow and this question will be coming out. This is always my stumbling block as I don't understand the steps I need to take to solve this problem. Can I get any help? Thanks in advance

I would calculate the "efficiency" of their work: $$e= \frac{H}{M\times D\times \frac{T}{24}}$$

$H$ - number of houses built
$M$ - men working
$D$ - days taken
$T$ - hours per day

Thus, we calculate $e$ first:

$$e= \frac{1}{24\times 45\times \frac{9}{24}}$$ $$e=\frac{1}{405}$$

Now you just plug in the data you got and use your calculated $e$.

$A)$ $$\frac{1}{405}=\frac{1}{18\times D \times \frac{8}{24}}$$ $$405= 6D$$ $$D=67.5$$

I think you can do $B)$ for yourself now.

B) Man-hours to build the house = 24*9*45 = 9720

let x = hours per day 20 men must work

20*x*48 = 9720

x= 9720/(20*48)= 10.125 hrs/day

Total men-hour-days required = 24*9*45 A) men = 18 , hour = 8 days = d = ? so 18*8*d = 24*9*45 d = 24*9*45/18*8 =67.5 days

B) men = 20, d = 48 , h = ? so 20*48*h = 24*9*45 h = 45*9/20*2 = 405/40 hours = 10 hour 7.5 minutes per day

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