A can do a job in 6 days and B in 8 days . They work together . Find A

1.	A can do a job in 6 days and B in 8 days . They work together . Find A's share if total amount given to them is Rs 3500.
Answer» align="ABSMIDDLE" alt="\sf{\BOLD{\green{\underline{\underline{Given}}}}}" class="latex-formula" id="TexFormula1" src="HTTPS://tex.z-dn.net/?F=%5Csf%7B%5Cbold%7B%5Cgreen%7B%5Cunderline%7B%5Cunderline%7BGiven%7D%7D%7D%7D%7D%20" title="\sf{\bold{\green{\underline{\underline{Given}}}}}"> A can do the work in 6 days B can do the work in 8 days Total amount = Rs. 3500 ______________________ $\sf{\bold{\green{\underline{\underline{To\:Find}}}}}$ A's share = ?? ______________________ $\sf{\bold{\green{\underline{\underline{Solution}}}}}$ ⠀⠀⠀⠀ $\sf{\red{\boxed{\bold{One\: day\: work =\dfrac{1}{Total\: time}}}}}$ ⠀⠀⠀⠀ $\sf:\implies \: {\bold{ A's\:one\: day: work\: = \: \dfrac{1}{6} }}$ ⠀⠀⠀⠀ $\sf:\implies \: {\bold{ B's\:one\: day: work\: = \: \dfrac{1}{8} }}$ ⠀⠀⠀⠀ Ratio of their works ⠀⠀⠀ $\sf:\implies \: {\bold{ A : B = \: \dfrac{\dfrac{1}{6}}{\dfrac{1}{8}}}}$ ⠀⠀⠀⠀ $\sf:\implies \: {\bold{ A : B = \: \dfrac{1\times 8}{6\times 1} }}$ ⠀⠀⠀⠀ $\sf:\implies \: {\bold{ A : B = \: \dfrac{8}{6} }}$ ⠀⠀⠀⠀ $\sf:\implies \: {\bold{ A : B = \: \dfrac{4}{3} }}$ ⠀⠀⠀⠀ let A's work be 4x and B's work be 3x ⠀⠀⠀⠀ ATQ:- ⠀⠀⠀⠀ 4x + 3x = 3500 ⠀⠀⠀⠀ 7x = 3500 ⠀⠀⠀⠀ x = 3500 / 7 ⠀⠀⠀⠀ x = 500 ⠀⠀⠀⠀ A's share = 4x = 4 × 500 = Rs. 2000 ____________________ $\sf{\bold{\green{\underline{\underline{Answer}}}}}$ ⠀⠀⠀⠀ A's shares = Rs. 2000

A can do a job in 6 days and B in 8 days . They work together . Find A's share if total amount given to them is Rs 3500.

Answer»

align="ABSMIDDLE" alt="\sf{\BOLD{\green{\underline{\underline{Given}}}}}" class="latex-formula" id="TexFormula1" src="HTTPS://tex.z-dn.net/?F=%5Csf%7B%5Cbold%7B%5Cgreen%7B%5Cunderline%7B%5Cunderline%7BGiven%7D%7D%7D%7D%7D%20" title="\sf{\bold{\green{\underline{\underline{Given}}}}}">

A can do the work in 6 days
B can do the work in 8 days
Total amount = Rs. 3500

______________________

$\sf{\bold{\green{\underline{\underline{To\:Find}}}}}$

A's share = ??

______________________

$\sf{\bold{\green{\underline{\underline{Solution}}}}}$

⠀⠀⠀⠀

$\sf{\red{\boxed{\bold{One\: day\: work =\dfrac{1}{Total\: time}}}}}$

⠀⠀⠀⠀

$\sf:\implies \: {\bold{ A's\:one\: day: work\: = \: \dfrac{1}{6} }}$

⠀⠀⠀⠀

$\sf:\implies \: {\bold{ B's\:one\: day: work\: = \: \dfrac{1}{8} }}$

⠀⠀⠀⠀

Ratio of their works

⠀⠀⠀

$\sf:\implies \: {\bold{ A : B = \: \dfrac{\dfrac{1}{6}}{\dfrac{1}{8}}}}$

⠀⠀⠀⠀

$\sf:\implies \: {\bold{ A : B = \: \dfrac{1\times 8}{6\times 1} }}$

⠀⠀⠀⠀

$\sf:\implies \: {\bold{ A : B = \: \dfrac{8}{6} }}$

⠀⠀⠀⠀

$\sf:\implies \: {\bold{ A : B = \: \dfrac{4}{3} }}$

⠀⠀⠀⠀

let A's work be 4x and B's work be 3x

⠀⠀⠀⠀

ATQ:-

⠀⠀⠀⠀

4x + 3x = 3500

⠀⠀⠀⠀

7x = 3500

⠀⠀⠀⠀

x = 3500 / 7

⠀⠀⠀⠀

x = 500

⠀⠀⠀⠀

A's share = 4x = 4 × 500 = Rs. 2000

____________________

$\sf{\bold{\green{\underline{\underline{Answer}}}}}$

⠀⠀⠀⠀

A's shares = Rs. 2000