Math, asked by sunilsahu74, 1 year ago

13. A and B can do a piece of work in 12 days, B and C in 15 days, and C and A in 20 days. How much time will A alone take to finish job?

Answers

Answered by Anonymous
71

Answer :-

A alone takes 30 days to finish the job.

Explanation :-

A and B can do a piece of work in 12 days

So A and B's 1 day work (A + B) = 1/12

B and C can do the same work in 15 days

So B and C's 1 fay work (B + C) = 1/15

C and A can do the same work in 20 days

C and A's 1 day work (C + A) = 1/20

We know that

2(A + B + C) = (A + B) + (B + C) + (C + A)

⇒ 2(A + B + C) = (1/12) + (1/15) + (1/20)

Taking LCM

⇒ 2(A + B + C) = (5 + 4 + 3)/60

⇒ 2(A + B + C) = 12/60

⇒ 2(A + B + C) = 1/5

⇒ A + B + C = (1/5) ÷ 2

⇒ A + B + C = (1/5) × (1/2)

⇒ A + B + C = 1/10

i.e A, B and C's 1 day work = 1/10

We know that

A's 1 day work = A, B and C's 1 day work - B and C's 1 day work

= (1/10) - (1/15)

Taking LCM

= (3 - 2)/30

= 1/30

i.e A's 1 day work = 1/30

So A alone takes 30 days to finish the job.

Answered by BrainlyConqueror0901
43

{\bold{\underline{\underline{Answer:}}}}

{\bold{\therefore A\:finish\:the\:job\:in\:30\:days}}

{\bold{\underline{\underline{Step-by-step\:explanation:}}}}

• In the given question information given about A and B can do a piece of work in 12 days, B and C in 15 days, and C and A in 20 days.

• We have to find time taken by A to finish job.

 \underline \bold{Given : } \\  \implies A \: and \: B \: do \: work \: in \: 12 \: days \\   \\ \implies B \: and \: C \: do \: work \: in \: 15 \: days \\  \\  \implies C\: and \: A \: do \: work \: in \: 20 \: days \\  \\  \underline \bold{To \: Find : } \\  \implies time \: taken \: by \: A \: to \: do \: work = ?

• According to given question :

 \bold{For \: A\: and \: B: } \\ \implies A + B = 12 \: days \\  \\  \implies In \: one \:  day(A + B) =  \frac{1}{12} -  -  -  -  - (1)  \\  \\ \bold{for \: B \: and \: C : } \\  \implies B + C= 15 \: days \\  \\  \implies In \: one \: day(B+ C) =  \frac{1}{15} -  -  -  -  - (2)  \\  \\  \bold{For \: C \: and \: A : } \\  \implies C + A= 20 \: days \\  \\  \implies In \: one \: day(C + A) =  \frac{1}{20} -  -  -  -  - (3)  \\  \\  \bold{According \: to \: question    : }  \\ \implies 2(A+ B + C) = (A + B) + (B + C) + (C+ A) \\  \\  \implies 2(A+ B+ C) =  \frac{1}{12}  +  \frac{1}{15}  +  \frac{1}{20}  \\  \\  \implies 2(A + B + C) =  \frac{5 + 4 + 3}{60}  \\  \\  \implies A + B+ C =  \frac{  \cancel{12} }{ \cancel{60 }\times 2}   \\  \\   \bold{\implies A + B + C =  \frac{1}{10} } \\  \\  \bold{Putting \: value \: of \: (B + C) \: from \: (2) }\\  \implies A +  \frac{1}{15}  =  \frac{1}{10}  \\  \\  \implies A =  \frac{1}{10}  -  \frac{1}{15}  \\  \\  \implies A =  \frac{3 - 2}{30}  \\  \\    \bold{\implies A=  \frac{1}{30} \: work \: in \: one \: day}  \\  \\  \bold{\therefore A\:finish\:the\:job\:in\:30\:days}

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