Question

The work done by (x-3) men in (2x+1) days and the work done by (2x+1) men in (x+4) days are in the ratio 3:10 . Find the value of x.
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Answer 1

$\bold{\large\green {\underline {\underline{Given:-}}}}$

• Ratio of work done by (x -3) men in (2x+1) days and the work done by (2x+1) men in (x+4) days = 3/4

$\bold{\large\green {\underline {\underline{Need \: to \: find:-}}}}$

• Value of x

$\bold{\large\green {\underline {\underline{Step \: by \: step \: explaination:-}}}}$

As we know the ratio of work done by men is 3:4. As this ratio is of total work done. Therefore, first we have to calculate the work done by men in 1 day. That will be calculated by multiplying (x-3) by (2x+1) and (2x+1) by (x+4).

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$\large\star{} \underline\mathfrak{Calculating \: work \: done \: by \: x - 3 \: men} \\ \: \: \: \: \: \: \: \implies \: ( \text{x} - 3) \times ( \text{2x + 1)} \\ \: \: \: \: \: \: \:\implies \: \text{or} \: ( \text{x - 3)(2x + 1)}$

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$\large\star{} \underline\mathfrak{Calculating \: work \: done \: by \: 2x + 1 \: men} \\ \: \: \: \: \: \: \: \implies \: ( \text{2x + 1)} \times ( \text{x + 4)} \\ \: \: \: \: \: \: \:\implies \: \text{or} \: ( \text{2x + 1)(x + 4)}$

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Noticing the given question here we have to divide the calculated amount of work done by each other which would be equal to the given ratio.

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$\large\star{} \underline\mathfrak{Calculating \: the \: value \: of \: x..} \\ \: \: \: \: \: \: \implies \: \frac{( \text{x - 3)(2x + 1)}}{ \text{(2x + 1)(x + 4)}} = \frac{3}{10}$

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$\large\star{} \underline\mathfrak{Opening \: brackets..} \\ \: \: \: \: \: \: \implies \: \frac{2x {}^{2} + \text{x} - \text{6x} - 3}{2x {}^{2} { + \text{8x} + x + 4}^{} } = \frac{3}{10}$

$\large\star{} \underline\mathfrak{Cross \: multiplying..} \\ \: \: \: \: \: \: \implies \: 10(2x {}^{2} + x - 6x - 3) = 3(2x {}^{2} + 8x + x + 4)$

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$\large\star{} \underline\mathfrak{Now..} \\ \: \: \: \: \: \: \implies \: 20x {}^{2} { - 50x} - 30 = 6x {}^{2} + 27x + 12 \\ \: \: \: \: \: \: \implies2x {}^{2} - 11x - 6 = 0 \\ \: \: \: \: \: \: \text{grouping \: terms}.. \\ \: \: \: \: \: \: ( \text{x - 6}) \text{(2x + 1)} = 0 \\ \: \: \: \: \: \: \implies \: \text{x} - 6 = 0 \\ \: \: \: \: \: \: \implies \: \text{x} = 6$

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$\bold{\large\green {\underline {\underline{Answer:-}}}}$

Value of x is 6

Reason~

Value of x is -1/2 also but it can't be accepted due to being in negative.