Question

the work done by X - 2 men in 4 x + 1 days and the work done by 4 x + 1 men in 2 x minus 3 days are in the ratio of 3 is to 8 find x
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Answer 1

Step-by-step explanation:

Total work done by (x- 2) men in (4x+1) days = (x- 2)(4x+1)

Total work done by (4x+1) men in (2x-3) days = (4x+1)(2x-3)

According to the given condition:

$\frac{(x- 2) (4x+1) }{(4x+1)(2x-3) } = \frac{3}{8} \\ \therefore \: \frac{(x- 2) }{(2x-3) } = \frac{3}{8} \\ \therefore \:8(x - 2) = 3(2x - 3) \\ \therefore \:8x - 16 = 6x - 9 \\ \therefore \:8x - 6x = 16 - 9 \\ \therefore \:2x = 7 \\ \huge \boxed{\therefore \:x = \frac{7}{22} }$

Answer 2

Given :

Work done by men is ( x - 2 ) in ( 4x + 1 ) day &

Work done by men is ( 4x + 1 ) in ( 2x - 3 ) day is in the ratio 3 : 8

Solution :

$(x - 2)(4x + 1)</u><u>:</u><u>(4x + 1)(2x - 3) = 3</u><u>:</u><u>8 \\ \\ \frac{(x - 2)(4x + 1)}{(4x + 1)(2x - 3)} = \frac{3}{8} \\ \\ \frac{ {4x}^{2} + x - 8x - 2}{8 {x}^{2} - 12x + 2x - 3} = \frac{3}{8} \\ \\ \frac{ {4x}^{2} - 7x - 2}{ {8x}^{2} - 10x - 3 } = \frac{3}{8} \\ \\ by \: \: cross \: \: multiplying \: \: \\ \\ 32 {x}^{2} - 56x - 16 = {24x}^{2} - 30x - 9 \\ \\ {32x}^{2} - 24 {x}^{2} - 56x + 30x - 16 + 9 = 0 \\ \\ 8 {x}^{2} - 26x - 7 = 0 \\ \\ 8 {x}^{2} - 28x + 2x - 7 = 0 \\ \\ 4x(2x - 7) + 1(2x - 7) = 0 \\ \\ (4x + 1)(2x - 7) = 0 \\ \\ 4x + 1 = 0 \\ 4x = - 1 \\ <strong><em>x = \frac{ - 1}{4}</em></strong> \\ \\ \\ 2x - 7 = 0 \\ 2x = 7 \\ <strong><em>x = \frac{7}{2}$

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