If 10 men can build a wall in 5 days then in how many days 5 men can build he same wall

2 thoughts on “If 10 men can build a wall in 5 days then in how many days 5 men can build he same wall”

1. Given :

   • If 10 men can build a wall in 5 days

   To Find:

   • In how many days will 5 men build the same wall

   Solution:

   Now,

   • Let the number of day taken by 5 men to build the wall be x days

   Table :

   [tex]\begin{gathered}\begin{gathered}\begin{gathered} \tiny\boxed{\begin{array}{ c |c} \frak{ \pmb{men}}& \rm{ \pmb{days}}\\ \dfrac{\qquad\qquad}{ \sf 10}&\dfrac{\qquad\qquad}{ \sf 5 \: days}& \\ \dfrac{\qquad\qquad}{ \sf 5}& \dfrac{\qquad\qquad}{ \sf x \: days} \end{array}}\end{gathered}& \\ \end{gathered}\end{gathered}[/tex]

   Here,

   • As the men of decrease the no. of days to do the work will increase so they are in inverse proportion

   When,

   • Two quantities are in inverse proportion we direct multiply the means and extreme terms on both the side and transpose numericals to find the value of the variables .

   [tex] \longrightarrow \tt \: 10 : 5 \propto 5 : x \\ \\ \\ \longrightarrow \tt \: 50 = 5x \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \longrightarrow \tt \: x = \cancel \frac{50}{5} \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \longrightarrow \tt { \boxed{ \frak{x = 10 \: days}}}[/tex]

   • Henceforth, 5 men can build the wall in 10 days

   Method 2

   We know,

   • 10 men can build up the wall in 5 days.

   So,

   • One man can build the wall in

   [tex] \longrightarrow \tt \: 10 \times 5 \: days \\ \\ \\ \longrightarrow \: { \pink{ \boxed{ \tt{ 50 days}}}}\: \: \: \:[/tex]

   Now,

   • 5 men can build the wall in

   [tex] \longrightarrow \tt \: 50 \div 5 \: days \\ \\ \\ \longrightarrow { \blue{ \boxed{ \tt{10days}} \star}} \: \: \: [/tex]

   Hence:

   • 5 men can build the wall in 10 days

   More to know:

   • When two ratios are in direct proportion

   [tex]{ \orange{ \star{ \boxed{ \tt \: {products \: of \: means \: = products \: of \: extremes}}}}}[/tex]

   Here,

   • You multiply the means of both sides and extremes of both the sides and find the value of the variable term transposition the numericals

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2. Correct Question :-

   If 10 men can build a wall in 5 days. Then in how many days 5 men can build the same wal?

   Given:

   • 10 men can build a wall in 5 days.

   To find:

   • How many days 5 men can build he same wall?

   Solution:

   • Let’s consider days Required for 5 men to build the same wall be x.

   10,5,5 & x are given to us.

   What to do?

   We need to find x.

   • 10,5,5,x

   Step-by-step explanation :-

   Here, 10 men can build a wall in 5 days. We have to find out x(how many days 5 men can build the same wall).

   → 10 : 5 = x : 5

   → 10/5 = x/5

   → 5x = 5 × 10

   → 5x = 50

   → x = 50/5

   → x = 10

   ∴ Hence, 5 men can build the same wall in 10 days.

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