Question

A protect can be completed by 75workers in 40days but protect manager brought 15more workers after 8days. In how many days will the remaining work be finished?​

Answer 1

$\\ \large \purple{ \sf \underline{ \: Question :-}}$

A protect can be completed by 75workers in 40days but protect manager brought 15more workers after 8days. In how many ?

$\\ \large \purple{ \sf \underline{ \: Given :-}}$

→A protect can be completed by 75workers in 40days

→ protect manager brought 15more workers after 8days.

$\\ \large \purple{ \sf \underline{ \: Solution :-}}$

$\\ \sf \: 1 \: worker \: does \: \: \bigg(\frac{1}{75} \bigg) \bigg( \frac{1}{40} \bigg) \: of \: work \: per \: day \: \:$

$\\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \: 1 \: After \: 8 \: days\:of\: using\:75\: workers, \:$

$\\ \sf \: \: \: \: \: : \implies \: (75)(8) \bigg( \frac{1}{75} \bigg) \bigg( \frac{1}{40} \bigg) \: = \: \frac{1}{5} \: of \: work \: hs \: been \: completed.$

$\\ \: \sf \: \frac{4}{5} \: of \: work \: is \: still \: outstanding \:$

$\\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: After \: 8 \: days,\: 15\:more\:workers\: has\: been\: hired, \\ \sf which\: brings\: the\: total\: to\: 90 \:workers.$

$\\ \\ \sf \: Let \: the \: number \: of \: additional \: days \: required \: be \: \red{ \bold{x}}.$

$\\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: (90)(x) \bigg ( \frac{1}{75} \bigg) \bigg( \frac{1}{40} \bigg) = \bigg( \frac{4}{5} \bigg)$

$\\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : \: \implies \: \frac{90}{3000} \times x \: = \: \frac{4}{5}$

$\\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : \: \implies \: \frac{3}{100} \times x \: = \: \frac{4}{5}$

$\\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : \: \implies \: x \: = \: \bigg( \frac{4}{5} \bigg) \times \bigg( \frac{100}{3} \bigg)$

$\\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : \implies \: x = \frac{400}{15}$

$\\ \sf \: \: \: \: \: \: \: \: \: \:\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : \implies \: x = \frac{80}{3}$

$\\ \sf \: \: \: \: \: \:\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : \implies \underline{ \boxed{ \pink{\frak{ \: x = 26 \: and \: \frac{2}{3} \: days}}}}$

$\: \\ \\ \sf \: \: \: \: \: \: \: \: \underline{ \: \: \: \bigstar \: \: In \: 26\frac{2}{3} \: days\: will \: the \: remaining \: work \: be \: finished. \: \: \: \: }$