Question

A and b can do a piece of work in 12 days b and c in 15 days c and a in 20 days how long would it take separately to do the same work

Answer 1

HEY GUYS YOUR ANSWER IS HERE !!!!!

 A + B=1/12; as both do 1/12 work in 12 days. similarly,
 B + C=1/15;
 A + C=1/20;
now adding above equations we get,
==>2(A + B +C)=1/12 + 1/15 +1/20;
==>2(A + B +C)=(10+8+6)/120; as, lcm= 120,
==>2(A + B +C)=24/120;
==>(A + B +C)=24/240;
==>(A + B +C)=1/10;
hence they all work in 10 days to complete.

I hope this answer is helpful for you .....

Answer 2

$\red{HEY\:BUDDY!!}$

HERE'S THE ANSWER..

______________________________

♠️ Here we go :)

▶️ A and B complete a work in 12 days

=> $\bold{ A+\:B=\:1 \div 12}$ ___( 1 )

▶️B and C complete it in 15 days

=> $\bold{ B+C=\:1 \div 15}$ ___( 2 )

▶️ A and C complete it in 20 days

=> $\bold{ A+C\:=\:1 \div 20}$ ___( 3 )

⏺️ Now adding all three equation

=> $\bold{ 2A+2B\:+ 2C\:=\:1 \div 12+1 \div 15+1 \div 20}$

⏺️ L.C.M. = 60

=> $\bold{ 2(A+B+C)\:=\:1 \div 12+1 \div 15+1 \div 20}$

=>$\bold{ 2(A+\B+C)\:=\:( 5+4+3) \div 60}$

=> $\bold{ (A+B+C)\:=\:12 \div 120}$

=> $\boxed{ (A+B+C)\:=\:1 \div 10}$___( 4 )

♠️ The all can do that work in ten days by working together...

♠️ Now we have to find ,how many day they take to do a work separately

⚓ For A { eqn ( 4 ) - ( 1 ) }

=> A = 1 / 10 - 1 / 15

⏺️ L.C.M. = 30

=> A = ( 3 - 2 ) / 30

=> $\boxed{ A\:=\: 1 \div 30}$

⚓ For B { eqn ( 4 ) - ( 3 ) }

=> B = 1 / 10 - 1 / 20

⏺️ L.C.M. = 20

=> B = ( 2 - 1 ) / 20

=> $\boxed{ B\:=\: 1 \div 20}$

⚓ For C { eqn ( 4 ) - ( 1 ) }

=> A = 1 / 10 - 1 / 12

⏺️ L.C.M. = 60

=> C = ( 6 - 5 ) / 30

=> $\boxed{ C\:=\: 1 \div 60}$

⏩ From above equations

⚫$\blue{A\: complete\:work\:in\:30\:days}$

⚫$\blue{B\: complete\:work\:in\: 20\:days}$

⚫$\blue{C\: complete\:work\:in\:60\:days}$

HOPE HELPED...

$\red{JAI\:HIND..}$

:)