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 .

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 .  Topic : - Ratios

Rylee · Answer

Answer:   Let the work done by one man in one day be : W     : implies   Work done by (x - 1) men in one day = W(x - 1)     : implies   Work done by (x - 1) men in (x + 1) days = W(x - 1)(x + 1)     : implies   Work done by (x + 2) men in one day = W(x + 2)     : implies   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      mathsf{: implies  dfrac{W(x - 1)(x + 1)}{W(x + 2)(x - 1)} =  dfrac{9}{10}}       mathsf{: implies  dfrac{(x + 1)}{(x + 2)} =  dfrac{9}{10}}      : implies   10(x + 1) = 9(x + 2)     : implies   10x + 10 = 9x + 18     : implies   10x - 9x = 18 - 10     : implies   x = 8

Ximena · Answer

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   :  -       longrightarrow sf  :  dfrac { ( x + 1 ) ( x - 1 ) } { ( x + 2 ) ( x - 1 ) } =  dfrac { 9 } { 10 }        longrightarrow sf  :  dfrac { { x }^{ 2 } - 1 } { { x }^{ 2 } - x + 2x - 2 } =  dfrac { 9 } { 10 }        longrightarrow sf  : 9( { x }^{ 2 } + x - 2 ) = 10( { x }^{ 2 } - 1 )        longrightarrow sf  : { 10x }^{ 2 } - 10 = { 9x }^{ 2 } + 9x - 18        longrightarrow sf  : { x }^{ 2 } - 9x + 8 = 0      Now ,    We have to factorize :-       longrightarrow sf  : { x }^{ 2 } - 8x - x + 8 = 0        longrightarrow sf  : x( x - 8 ) - 1( x - 8 ) = 0        longrightarrow sf  : ( x - 8 ) ( x - 1 ) = 0        longrightarrow sf  : x = 8 , 1      Hence ,     The value of x of 8 , 1

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

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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 .