Question

A can do a job in 20 days, B in 30 days and C in 60 days.If B And C help A on the third day,in how long that work be completed?

Answer mathdude​

Answer 1

$\large\underline{\sf{Solution-}}$

Given that,

• A can do a job in 20 days.

• B can do the same job in 30 days.

• C can do the same job in 60 days.

• B and C help A on the third day.

So,

$\rm \: {A'}^{s} \: 1 \: day \: work \: = \: \frac{1}{20}$

$\rm \: {B'}^{s} \: 1 \: day \: work \: = \: \frac{1}{30}$

$\rm \: {C'}^{s} \: 1 \: day \: work \: = \: \frac{1}{60}$

So,

$\rm \: {A'}^{s} \: 2\: day \: work \: = \: 2 \times \frac{1}{20} = \frac{1}{10}$

$\rm \: {B'}^{s} \:2\: day \: work \: = \: 2 \times \frac{1}{30} = \frac{1}{15}$

$\rm \: {C'}^{s} \:2\: day \: work \: = \: 2 \times \frac{1}{60} = \frac{1}{30}$

As it is given that, on third day A is assist by B and C.

So, total work done in three days is equals to work done by A in 3 days + 1 day work of B + 1 day work of C.

So, work completed in three days is

$\rm \: = \: \dfrac{1}{10} + \dfrac{1}{20} + \dfrac{1}{30} + \dfrac{1}{60}$

$\rm \: = \: \dfrac{6 + 3 + 2 + 1}{60}$

$\rm \: = \: \dfrac{12}{60}$

$\rm \: = \: \dfrac{1}{5}$

So,

Number of days to complete the work = 3 × 5 = 15 days.