Question

the ratio of work done by (x+2) men in (x-2) days to that of (x-1) men in (x+1) days is 4:5 , the value of x is

Answer 1

4 will be the answer

Answer 2

Given :

Work done by men is ( x + 2 ) in ( x - 2 ) days &

Work done by men is ( x - 1 ) in ( x + 1 ) days is in the ratio 4 : 5

Solution :

$(x + 2)(x - 2)</u><u>:</u><u>(x - 1)(x + 1) = 4</u><u>:</u><u>5 \\ \\ \frac{(x + 2)(x - 2)}{(x - 1)(x + 1)} = \frac{4}{5} \\ \\ numerator \: \: and \: \: denominator \: \: is \: \: the \: \: form \: \: (x + y)(x - y) = {x}^{2} - {y}^{2} \\ \\ \frac{ {x}^{2} - {2}^{2} }{ {x}^{2} - {1}^{2} } = \frac{4}{5} \\ \\ \frac{ {x}^{2} - 4}{ {x}^{2} - 1} = \frac{4}{5} \\ \\ by \: \: cross \: \: multiplying \: \: \\ \\ 5 {x}^{2} - 20 = 4 {x}^{2} - 4 \\ \\ 5 {x}^{2} - {4x}^{2} - 20 + 4 = 0 \\ \\ {x}^{2} - 16 = 0 \\ \\ {x}^{2} - {4}^{2} = 0 \\ \\ (x + 4)(x - 4) = 0 \\ \\ \\ x + 4 = 0 \\ x = - 4 \\ \\ \\ x - 4 = 0 \\ x = 4$

The value of x is 4

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