Question

Both of lalima and romen clean their garden.if lalima works for 4 days and romen work for 3 days,then 2/3 part of the work is complete.Again,if lalima work for 3 days and romen work for 6 days then 11/2 part of the work is completed.lets us form the simultaneous equation and write the number of days require to complete the work separately by lalima and romen by calculating the Solution?​

Answer 1

Answer:

Answer:

$\huge\ \sf{\red {[[«\: คꈤ \mathfrak Sฬєя \: » ]]}}$

$\sf \: Let \:the \:whole \: work \:done \:by \:Lalima \:be \: x \: and \: Romen \:be \:y$

$\sf \: work \: done \:by \:lalima \:in \:1 \:day \:= 1÷x$

$\ = \dfrac{1}{x}$

$\sf \: work \:done \:by \:lalima \: in \:4 \:days \:= 1/x ×4$

$\ = \dfrac{4}{x}$

$\sf \: work \:done \:by \: Romen \: in \:1 \:day \:= 1÷y$

$\ = \dfrac{1}{y}$

$\sf \: work \:done \:by \:the \:Romen \:in \: 3 \: days \:=1/y×3$

$\ = \dfrac{3}{y}$

$\sf \: Both \:worked \:and \:completed \:2/3 \:part \: of \:work$

$\ {\dfrac{4}{x}+\dfrac{3}{y} = \dfrac{2}{3}}$ --------- equation 1

$\sf \: again,$

$\sf \: work \: done \: by \:lalima \: in \: 3 \:days \:= 1/x×3$

$\ = \dfrac{3}{x}$

$\sf \: work \: done \: by \: the \: Romen \:in \:3 \: days \:=1/y×6$

$\ = \dfrac{6}{y}$

$\sf \: Both \:worked \:and \:completed \:11/12 \: part \: of \: work$

$\ {\dfrac{3}{x}+\dfrac{6}{y} = \dfrac{11}{,12}}$ $\sf- ------ equation \: 2$

From equation 1 and 2

$\ {\dfrac{4}{x}+\dfrac{3}{y} = \dfrac{2}{3}}$

$\ {\dfrac{3}{x}+\dfrac{6}{y} = \dfrac{11}{,12}}$

$\sf \: - \: \: - \: \: - {by \: subtracting}$

___________

$\ 0x - {\dfrac{15}{y} =-\dfrac{5}{3}}$

$\ ⟹{\dfrac{1}{y} =\dfrac{5}{3×15}}$

$\ ⟹{\dfrac{1}{y} =\dfrac{1}{9}}$

$\sf \: ⟹\: y=9$

$\sf \: putting \:the \: value \: of \:9 \: in \:equation \: 1 ,we \:get$

$\ {\dfrac{4}{x}+\dfrac{3}{9} = \dfrac{2}{3}}$

$\ ⟹{\dfrac{4}{x}= \dfrac{2}{3} -\dfrac{3}{9}}$

$\ ⟹{\dfrac{4}{x} = \dfrac{1}{3}}$

$\ ⟹{\dfrac{1}{x} = \dfrac{1}{12}}$

$\sf \: ⟹x=12$

$\sf \: Therefore,\:Lalima\:required\: 12\:days\:for\:complete\:the\:work\:and\:Romen\:required\:9\:days \:to\:complete\:$