Question

A&b can complete a work meeting n 10 days, b&c in 15 days, A&b in 12 days in how many days a, b and c together complete the task

Answer 1

$\mathfrak{\huge{Answer:}}$

$\mathbb{GIVEN}$

A and B can complete the work in -》 10 days

B and C can complete the work in -》 12 days

A and C can complete the work in -》 15 days

$\mathbb{TO\:FIND}$

The number of days taken by A, B and C to complete the task together.

$\mathbb{METHOD}$

We are given with the numbers of days taken by A, B and C in pairs. Also, if we notice the pattern, we can observe that each of them has been considered twice. Now:

A and B 's one day work = $\tt{\frac{1}{10}}$

B and C 's one day work = $\tt{\frac{1}{12}}$

A and C 's one day work = $\tt{\frac{1}{15}}$

Add these three equations together :

=》 $\tt{\frac{1}{10}}$+ $\tt{\frac{1}{12}}$ + $\tt{\frac{1}{15}}$

=》 $\tt{\frac{6 + 4 + 5}{60}}$

=》 $\tt{\frac{15}{60}}$

=》 $\tt{\frac{1}{4}}$

Now, we've just seen the R.H.S of the equation. Let's now see the L.H.S. :

=》 A + B + B + C + A + C

=》 2 ( A + B + C )

We need to find the number of days taken by $\bf{A,B\:and\:C}$ together. Put the L.H.S. and R.H.S. together :

=》 2 ( A + B + C ) = $\tt{\frac{1}{4}}$

=》 A + B + C = $\tt{\frac{1}{4 \times 2}}$

=》 A + B + C = $\tt{\frac{1}{8}}$

The answer we've got is the one day work of A, B and C together.

The number of days taken = 8 days

Thus, the answer will be $\tt{\huge{8\:days}}$