Question

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A and B can do a piece of work in 10 days ; B and C in 15 days ; C and A in 12 days. How long would A and B take separately to do the same work? ​

Answer 1

QUESTION:-

A and B can do a piece of work in 10 days ; B and C in 15 days ; C and A in 12 days. How long would A and B take separately to do the same work? ​

EXPLANATION:-

==>A+B=10 DAYS------1

==>B+C=15 DAYS-------1

==>C+A=12 DAYS---------1

From the above equation we can derive A's work :-

A=10-B

A=12-C

So both the equation are now equal

10-B=12-C

-B=12-C-10

-B=2-C

B=C-2

B+2=C

SUBSTITUTE THIS B+2=C IN EQ-2

B+(B+2)=15

2B+2=15

2B=13

B=13/2

B=6.5  

SO B CAN DO WORK IN 6.5 DAYS

SUBSTITUTE THE B'S WORK IN EQ-1

A+B=10

A+6.5=10

A=10-6.5

A=3.5 DAYS

SO B CAN DO WORK IN 6.5 DAYS OR 6 DAYS AND 12 HOURS WHILE A CAN DO WORK IN 3.5 DAYS OR 3 DAYS AND 12 HOURS

Answer 2

$\red \bigstar \: \sf GIVEN$

➝ A and B can complete the work in 10 days.

➝ B and C in 15 days.

➝ C and A in 12 days.

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$\pink \bigstar \: \sf \: SOLUTION$

➝ A and B can complete the work in 10 days.

∴ (A and B) 's one day work = 1/10 part.

◈ Similarly,

➝ (B and C)'s one day work = 1/15 part.

➝ (C and A)'s one day work = 1/12 part.

◈ Adding up, we get

2 (A and B and C)'s work in 1 day.

$\sf = ( \dfrac{1}{10} + \dfrac{1}{15} + \dfrac{1}{12} ) \: \: part$

$\sf \: = \dfrac{6 + 4 + 5}{60} = \dfrac{ \cancel{15}}{ \cancel{60}} = \dfrac{1}{4} \: part$

∴ (A and B and C ) can do in one day =

$\sf \: \: \dfrac{1}{4} \times \dfrac{1}{2} = \dfrac{1}{8} \: part$

◈ Now, part of the work that A can do it in 1 day

${ \sf {\red{ = (1 \: day \: work \: of \: a \: and \: b \: and \: c) }}} - \\ \sf \red{(1 \: day \: work \: of \: b \: and \: c)\: }$

$\sf \: = \dfrac{1}{8} - \dfrac{1}{15} = \dfrac{15 - 8}{120} = \dfrac{7}{120} \: part$

∴ A can complete the work in ( 1× 120/7) days, i.e. 120/7 i.e. 17 1/7 days

$\sf \pink{∴A \: can \: complete \: the \: work \: in 17</h3><p>1/7 days}$

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◈ Similarly,

Part of the work that B can do it in 1 day

= ( 1 day work of A and B and C) - ( 1 day work of A and C)

= 1/8 - 1/12 = 3-2/24 = 1/24

∴ B can complete the work in ( 1× 24/1) days, i.e. 24 days.

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