Question

8. A pond will be dug in our locality. 24 men need 12 days to cut that pond. Let's
find out the proportion and find relation how many men will be needed to dig that
pond in 8 days.​

Answer 1

$\huge{\blue{\bold{\underline{\underline{Answer :}}}}}$

$\:\:$

$\large{\green{\underline \bold{\tt{Given :-}}}}$

$\:\:$

• 24 men took 12 days to cut the pond

$\:\:$

$\large{\red{\underline \bold{\tt{To \: Find :-}}}}$

$\:\:$

• Number of men required to finish the work in 8 days

$\:\:$

$\large{\orange{\underline{\tt{Solution :-}}}}$

$\:\:$

• Let the total men required to finish the work in 8 days be "x"

$\:\:$

Method I

$\:\:$

$\underline{\bold{\texttt{Work done in one day :}}}$

$\:\:$

➠ $\sf \dfrac { 1 } { 12 }$

$\:\:$

$\underline{\bold{\texttt{Work done by one man :}}}$

$\:\:$

➠ $\sf \dfrac { 1 } { 24 }$

$\:\:$

$\underline{\bold{\texttt{Work done by one man in one day :}}}$

$\:\:$

➠ $\sf \dfrac { 1 } { 24 } \times \dfrac { 1 } { 12 }$

$\:\:$

➠ $\bf \dfrac { 1 } { 288 }$

$\:\:$

$\underline{\bold{\texttt{One man's 8 days work :}}}$

$\:\:$

➠ $\sf \dfrac { 1 } { 288 } \times 8$

$\:\:$

$\underline{\bold{\texttt{"x" men 8 day work :}}}$

$\:\:$

➠ $\sf \dfrac { 1 } { 288 } \times 8 \times x$

$\:\:$

As "x" men can finish the work in 8 days

$\:\:$

So,

$\:\:$

➜ $\sf \dfrac { 1 } { \cancel {288} } \times \cancel 8 \times x = 1$

$\:\:$

➜ $\sf \dfrac { 1 } { 36 } \times x = 1$

$\:\:$

➨ x = 36 men

$\:\:$

• Hence , 36 men can finish the work in 8 days

$\:\:$

Method II

$\:\:$

〚 We can clearly observe that when the number of men will increase the days required to finish the work will decrease. Therefore it is a case of inverse proportion 〛

$\:\:$

So,

$\:\:$

• Let the number of men required to finish the work in 8 days be "x"

$\:\:$

➜ 24:x = 8:12

$\:\:$

➜ $\sf \dfrac { 24 } { x } = \dfrac { 8 } { 12 }$

$\:\:$

➜ $\sf 24 \times 12 = 8 \times x$

$\:\:$

➜ 288 = 8x

$\:\:$

➜ $\sf x = \dfrac { 288 } { 8 }$

$\:\:$

➨ x = 36

$\:\:$

• Hence 36 men can finish the work in 8 days

Answer 2

$\huge{\blue{\bold{\underline{\underline{Answer :}}}}}$

$\:\:$

$\large{\green{\underline \bold{\tt{Given :-}}}}$

$\:\:$

• 24 men took 12 days to cut the pond

$\:\:$

$\large{\red{\underline \bold{\tt{To \: Find :-}}}}$

$\:\:$

• Number of men required to finish the work in 8 days

$\:\:$

$\large{\orange{\underline{\tt{Solution :-}}}}$

$\:\:$

Let the total men required to finish the work in 8 days be "x"

$\:\:$

Method I

$\:\:$

$\underline{\bold{\texttt{Work done in one day :}}}$

$\:\:$

➠ $\sf \dfrac { 1 } { 12 }$

$\:\:$

$\underline{\bold{\texttt{Work done by one man :}}}$

$\:\:$

➠ $\sf \dfrac { 1 } { 24 }$

$\:\:$

$\underline{\bold{\texttt{Work done by one man in one day :}}}$

$\:\:$

➠ $\sf \dfrac { 1 } { 24 } \times \dfrac { 1 } { 12 }$

$\:\:$

➠ $\bf \dfrac { 1 } { 288 }$

$\:\:$

$\underline{\bold{\texttt{One man's 8 days work :}}}$

$\:\:$

➠ $\sf \dfrac { 1 } { 288 } \times 8$

$\:\:$

$\underline{\bold{\texttt{"x" men 8 day work :}}}$

$\:\:$

➠ $\sf \dfrac { 1 } { 288 } \times 8 \times x$

$\:\:$

As "x" men can finish the work in 8 days

$\:\:$

So,

$\:\:$

➜ $\sf \dfrac { 1 } { \cancel {288} } \times \cancel 8 \times x = 1$

$\:\:$

➜ $\sf \dfrac { 1 } { 36 } \times x = 1$

$\:\:$

➨ x = 36 men

$\:\:$

Hence , 36 men can finish the work in 8 days

$\:\:$

Method II

$\:\:$

〚 We can clearly observe that when the number of men will increase the days required to finish the work will decrease. Therefore it is a case of inverse proportion 〛

$\:\:$

So,

$\:\:$

Let the number of men required to finish the work in 8 days be "x"

$\:\:$

➜ 24:x = 8:12

$\:\:$

➜ $\sf \dfrac { 24 } { x } = \dfrac { 8 } { 12 }$

$\:\:$

➜ $\sf 24 \times 12 = 8 \times x$

$\:\:$

➜ 288 = 8x

$\:\:$

➜ $\sf x = \dfrac { 288 } { 8 }$

$\:\:$

➨ x = 36

$\:\:$

• Hence 36 men can finish the work in 8 days