Question

Ten men, working for 6 days of 10 hours finish 5/21 of a piece of work. How many men working at the same rate and for the number of hours each day, will be required to complete the remaining work in 8 days​

Answer 1

$\bigstar\purple{\boxed{\large\bf{\leadsto 24\:men}}}$

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$\large\sf\underline{Given: }$

• ➠ 10 men, working for 6 days of 10 hours finish $\dfrac{5}{21}$ of a piece of work
• ➠ 600 hrs to complete $\dfrac{5}{21}$ of work.

$\large\sf\underline{To\:find: }$

• ➠The number of men working at the same rate and for the number of hours each day to complete the remaining work in 8 days.

$\large\sf\underline{ Some\: abbrivations: }$

• ➠ M = number of men
• ➠ D = number of days
• ➠ H = number of hours worked per day
• ➠ N = work done

❍ Lets first find the number of working hours required to complete $\dfrac{5}{21}$ of work.

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❍ Let the total number of hours required to complete the work be x then :

ㅤㅤㅤㅤㅤ$\sf{\longrightarrow (x) =\dfrac{5}{21}\div 600}$

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ㅤㅤㅤㅤㅤ$\sf{\longrightarrow (x)=600\times\dfrac{21}{5}}$

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ㅤㅤㅤㅤㅤ$\sf{\longrightarrow (x)=\cancel{\dfrac{12600}{5}}}$

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ㅤㅤㅤㅤㅤ$\sf{\longrightarrow (x)=2520\:hours}$

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❍ So the remaining work $\sf{(x)-\dfrac{5}{21}}$ is :

ㅤㅤㅤㅤㅤ$\sf{\longrightarrow \dfrac{16}{21}x}$

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ㅤㅤㅤㅤㅤ$\sf{\longrightarrow \dfrac{16}{22}\times 2520}$

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ㅤㅤㅤㅤㅤ$\sf{\longrightarrow \cancel{\dfrac{40320}{21}}}$

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ㅤㅤㅤㅤㅤ$\sf{\longrightarrow 1920}$

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➨ 1920 hrs required to complete remaining $\dfrac{16}{21}$ of work

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❍ Equation to find number of men required :

ㅤㅤㅤㅤㅤ$\underline{\boxed{\bf{MDH=N }}}$

ㅤㅤㅤㅤㅤ$\sf{\longrightarrow MDH=1920}$

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ㅤㅤㅤㅤㅤ$\sf{\longrightarrow M\times 8\times 10=1920}$

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ㅤㅤㅤㅤㅤ$\sf{\longrightarrow M = \cancel{\dfrac{1920}{80}}}$

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ㅤㅤㅤㅤㅤ$\sf{\longrightarrow M=24}$

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$\large\sf\orange{\underline{\dag Hence,\:24 \:men \: are \: required. }}$

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