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Question Number 106176 by john santu last updated on 03/Aug/20

If 20 men can lay 36m of a pipe in 8 hours. How long would 25 men take to lay the next 54m of the pipe?

$$\mathrm{If}\:\mathrm{20}\:\mathrm{men}\:\mathrm{can}\:\mathrm{lay}\:\mathrm{36m}\:\mathrm{of}\:\mathrm{a}\:\mathrm{pipe} \\ $$$$\mathrm{in}\:\mathrm{8}\:\mathrm{hours}.\:\mathrm{How}\:\mathrm{long}\:\mathrm{would}\:\mathrm{25} \\ $$$$\mathrm{men}\:\mathrm{take}\:\mathrm{to}\:\mathrm{lay}\:\mathrm{the}\:\mathrm{next}\:\mathrm{54m}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{pipe}? \\ $$

Commented by john santu last updated on 03/Aug/20

thank you

$$\mathrm{thank}\:\mathrm{you}\: \\ $$

Answered by nimnim last updated on 03/Aug/20

men hr metre 20 8 36 25 x 54 ∴ x=((20×8×54)/(25×36))=((48)/5) ⇒x=9(3/5)hrs=9hrs 36min★

$${men}\:\:\:\:\:\:{hr}\:\:\:\:\:\:\:{metre} \\ $$$$\:\mathrm{20}\:\:\:\:\:\:\:\:\:\:\:\mathrm{8}\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{36} \\ $$$$\:\mathrm{25}\:\:\:\:\:\:\:\:\:\:\:{x}\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{54} \\ $$$$\:\:\:\therefore\:\:{x}=\frac{\mathrm{20}×\mathrm{8}×\mathrm{54}}{\mathrm{25}×\mathrm{36}}=\frac{\mathrm{48}}{\mathrm{5}} \\ $$$$\:\:\Rightarrow{x}=\mathrm{9}\frac{\mathrm{3}}{\mathrm{5}}{hrs}=\mathrm{9}{hrs}\:\mathrm{36}{min}\bigstar \\ $$

Answered by 1549442205PVT last updated on 04/Aug/20

The time using for 1 men lay 1 m of the pipe be: ((20×8)/(36))(hours).Hence,the time for 1 men lay 54 m of the pipe be ((20×8)/(36))×54(hours).It follows that the time for 25 men lay 54 m of the pipe be (((20×8)/(36))×54)/25=((4×5×8×9×6)/(4×9×5×5))=((6×8)/5)=9(3/5)(hour) =9 hours and 36 minuts

$$\mathrm{The}\:\mathrm{time}\:\mathrm{using}\:\mathrm{for}\:\mathrm{1}\:\mathrm{men}\:\mathrm{lay}\:\mathrm{1}\:\mathrm{m}\:\mathrm{of}\:\mathrm{the}\:\:\mathrm{pipe}\:\mathrm{be}: \\ $$$$\frac{\mathrm{20}×\mathrm{8}}{\mathrm{36}}\left(\mathrm{hours}\right).\mathrm{Hence},\mathrm{the}\:\mathrm{time}\:\mathrm{for}\:\mathrm{1}\:\mathrm{men} \\ $$$$\mathrm{lay}\:\mathrm{54}\:\mathrm{m}\:\mathrm{of}\:\mathrm{the}\:\mathrm{pipe}\:\mathrm{be} \\ $$$$\frac{\mathrm{20}×\mathrm{8}}{\mathrm{36}}×\mathrm{54}\left(\mathrm{hours}\right).\mathrm{It}\:\mathrm{follows}\:\mathrm{that}\:\mathrm{the}\: \\ $$$$\mathrm{time}\:\mathrm{for}\:\mathrm{25}\:\mathrm{men}\:\mathrm{lay}\:\mathrm{54}\:\mathrm{m}\:\mathrm{of}\:\mathrm{the}\:\mathrm{pipe}\:\mathrm{be} \\ $$$$\left(\frac{\mathrm{20}×\mathrm{8}}{\mathrm{36}}×\mathrm{54}\right)/\mathrm{25}=\frac{\mathrm{4}×\mathrm{5}×\mathrm{8}×\mathrm{9}×\mathrm{6}}{\mathrm{4}×\mathrm{9}×\mathrm{5}×\mathrm{5}}=\frac{\mathrm{6}×\mathrm{8}}{\mathrm{5}}=\mathrm{9}\frac{\mathrm{3}}{\mathrm{5}}\left(\mathrm{hour}\right) \\ $$$$=\mathrm{9}\:\boldsymbol{\mathrm{hours}}\:\:\boldsymbol{\mathrm{and}}\:\mathrm{36}\:\boldsymbol{\mathrm{minuts}} \\ $$

Answered by Don08q last updated on 03/Aug/20

Assuming equal rates of work, Number of man−hours ≡ Workdone 20 men ×8 hours ≡ 36 m 25 men × n hours ≡ 54 m ⇒ ((20 × 8)/(25 × n)) = ((36)/(54)) n = ((20 × 8 × 54)/(25 × 36 )) n = 9.6 hours n = 9 hours, 36 minutes.

$${Assuming}\:{equal}\:{rates}\:{of}\:{work}, \\ $$$$\:\mathrm{Number}\:\mathrm{of}\:\mathrm{man}−\mathrm{hours}\:\equiv\:\mathrm{Workdone} \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{20}\:{men}\:×\mathrm{8}\:{hours}\:\equiv\:\mathrm{36}\:{m} \\ $$$$\:\:\:\:\:\:\:\mathrm{25}\:{men}\:×\:\boldsymbol{{n}}\:{hours}\:\equiv\:\mathrm{54}\:{m} \\ $$$$\Rightarrow\:\:\:\:\:\:\frac{\mathrm{20}\:×\:\mathrm{8}}{\mathrm{25}\:×\:\boldsymbol{{n}}}\:=\:\frac{\mathrm{36}}{\mathrm{54}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{{n}}\:\:\:=\:\:\:\frac{\mathrm{20}\:×\:\mathrm{8}\:×\:\mathrm{54}}{\mathrm{25}\:×\:\mathrm{36}\:} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{{n}}\:\:\:=\:\:\mathrm{9}.\mathrm{6}\:{hours} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{{n}}\:\:=\:\:\mathrm{9}\:{hours},\:\mathrm{36}\:{minutes}. \\ $$

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