Share

# A and B can do a piece of work in 18 days; B and C in 24 days and A and C in 36 days. In what time can they do it, all working together? - Mathematics

Course
ConceptTime and Work

#### Question

A and B can do a piece of work in 18 days; B and C in 24 days and A and C in 36 days. In what time can they do it, all working together?

#### Solution

$\text{ Time taken by } \left( A + B \right) \text{ to do the work = 18 days }$
$\text{ Time taken by } \left( B + C \right) \text{ to do the work = 24 days }$
$\text{ Time taken by } \left( A + C \right) \text{ to do the work = 36 days }$
$\text{ Now } ,$
$\text{ Work done by } \left( A + B \right) = \frac{1}{18}$
$\text{ Work done by } \left( B + C \right) = \frac{1}{24}$
$\text{ Work done by } \left( A + C \right) = \frac{1}{36}$
$\therefore \text{ Work done together } = \left( A + B \right) + \left( B + C \right) + \left( A + C \right)$
$= \frac{1}{18} + \frac{1}{24} + \frac{1}{36}$
$= \frac{4 + 3 + 2}{72} = \frac{9}{72}$
$= \frac{1}{8}$
$\therefore \text{ Work done together } = 2\left( A + B + C \right) = \frac{1}{8}$
$\therefore \text{ Work done by } \left( A + B + C \right) = \frac{1}{16}$
$\text{ Thus, together they can finish the work in 16 days } .$

Is there an error in this question or solution?

#### APPEARS IN

Solution A and B can do a piece of work in 18 days; B and C in 24 days and A and C in 36 days. In what time can they do it, all working together? Concept: Time and Work.
S