If the work done by x – 1 men in x + 1 days is to the work done by x + 2 men in x – 1 days in the ratio of 9 : 10 , find x .

2 thoughts on “If the work done by x – 1 men in x + 1 days is to the work done by x + 2 men in x – 1 days in the ratio of 9 : 10 , find x .<br />”

1. Answer:

   Let the work done by one man in one day be : W

   [tex]:\implies[/tex] Work done by (x – 1) men in one day = W(x – 1)

   [tex]:\implies[/tex] Work done by (x – 1) men in (x + 1) days = W(x – 1)(x + 1)

   [tex]:\implies[/tex] Work done by (x + 2) men in one day = W(x + 2)

   [tex]:\implies[/tex] Work done by (x + 2) men in (x – 1) days = W(x + 2)(x – 1)

   Given – Ratio of work done by (x – 1) men in (x + 1) days to that of (x + 2) men in (x – 1) days is 9 : 10

   [tex]\mathsf{:\implies \dfrac{W(x – 1)(x + 1)}{W(x + 2)(x – 1)} = \dfrac{9}{10}}[/tex]

   [tex]\mathsf{:\implies \dfrac{(x + 1)}{(x + 2)} = \dfrac{9}{10}}[/tex]

   [tex]:\implies[/tex] 10(x + 1) = 9(x + 2)

   [tex]:\implies[/tex] 10x + 10 = 9x + 18

   [tex]:\implies[/tex] 10x – 9x = 18 – 10

   [tex]:\implies[/tex] x = 8

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2. Question:-

   • If the work done by x – 1 men in x + 1 days is to the work done by x + 2 men in x – 1 days in the ratio of 9:10, find x.

   To Find:–

   • Find the value of x.

   Solution:–

   [tex]\longrightarrow\sf \: \dfrac { ( x + 1 ) ( x – 1 ) } { ( x + 2 ) ( x – 1 ) } = \dfrac { 9 } { 10 } [/tex]

   [tex]\longrightarrow\sf \: \dfrac { { x }^{ 2 } – 1 } { { x }^{ 2 } – x + 2x – 2 } = \dfrac { 9 } { 10 } [/tex]

   [tex]\longrightarrow\sf \: 9( { x }^{ 2 } + x – 2 ) = 10( { x }^{ 2 } – 1 ) [/tex]

   [tex]\longrightarrow\sf \: { 10x }^{ 2 } – 10 = { 9x }^{ 2 } + 9x – 18 [/tex]

   [tex]\longrightarrow\sf \: { x }^{ 2 } – 9x + 8 = 0 [/tex]

   Now ,

   We have to factorize:-

   [tex]\longrightarrow\sf \: { x }^{ 2 } – 8x – x + 8 = 0 [/tex]

   [tex]\longrightarrow\sf \: x( x – 8 ) – 1( x – 8 ) = 0 [/tex]

   [tex]\longrightarrow\sf \: ( x – 8 ) ( x – 1 ) = 0 [/tex]

   [tex]\longrightarrow\sf \: x = 8 , 1 [/tex]

   Hence ,

   • The value of x of 8 , 1

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