Question

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 1

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

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

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

• A's share = ??

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

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

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

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

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• Ratio of their works

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

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

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

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

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

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ATQ:-

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4x + 3x = 3500

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7x = 3500

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x = 3500 / 7

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x = 500

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A's share = 4x = 4 × 500 = Rs. 2000

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

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• A's shares = Rs. 2000