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

Answer 1

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

Answer 2

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