Question

A and B can perform a task in 30 , 40 days. They work together for some days, B drop out of work A complet the remaining job in 9 days after how many days B drop out of work? solution

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Answer 1

Question :-

A and B can perform a task in 30 , 40 days. They work together for some days, B drop out of work A complet the remaining job in 9 days after how many days B drop out of work? solution.

Solution :-

Given :

• A and B can perform a task in 30 , 40 days.
• They work together for some days, B drop out of work.
• A complet the remaining job in 9 days.

Need to find :

• after how many days B drop out of work ?

Let after d days b dropped out of work that is A and B work together for d days.

According to the question,

1 day work of A

$\sf{ \frac{1}{30} \: \: \: \: \: \: \: \: \: \: \: \: \: \: ....\{given \} }$

1 day work of B

$\sf{ \frac{1}{40} \: \: \: \: \: \: \: \: \: ...\{given \} }$

Then A & B work together

$\sf : \longmapsto{ \frac{1}{30} + \frac{1}{40} } \\ \\ \sf : \longmapsto{ \frac{40 + 30}{1200} } \: \\ \\ \sf : \longmapsto{ \frac{70}{120} } \: \: \: \: \: \: \: \: \\ \\ \sf : \longmapsto{ \frac{7}{120} } \: \: \: \: \: \: \:$

By given information : d days work A and B together

$\sf : \longmapsto{ \frac{7}{120} \times d}$

Remaining work after d days

$\sf : \longmapsto{1 - \frac{7d}{120} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf : \longmapsto{ \frac{120 - 7d}{120} \: \: \: \: \: \: \: \: \: \: \: \: \: \: .... \bigg\{equation \: (1) \bigg\}}$

9 days work of A

$\sf : \longmapsto{ \frac{1}{30} \times 9 } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bigg\{equation \: (2) \bigg\}$

Now,

Equation (1) = Equation (2)

$\sf : \longmapsto{ \frac{120 - 7d}{120} = \frac{1}{30} \times 9 } \\ \\ \sf : \longmapsto{ \frac{ \cancel{30}(120 - 7d)}{ \cancel{120}} = 9 } \: \: \: \\ \\ \sf : \longmapsto{ \frac{120 - 7d}{4} = 9 } \: \: \: \: \: \: \: \: \: \: \\ \\ \sf : \longmapsto{120 - 7d = 9 \times 4} \: \: \: \\ \\ \sf : \longmapsto{7d = 120 - 36} \: \: \: \: \: \: \: \: \\ \\ \sf : \longmapsto{7d = 84} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf : \longmapsto{d = \cancel\frac{84}{7} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf : \longmapsto{d = 12} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Hence, B dropped out of work after 12 days.

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