Question

If a and b work together, they will complete a job in 7.5 days. however, if a works alone and completes half the job and then b takes over and completes the remaining half alone, they will be able to complete the job in 20 days. how long will b alone take to do the job if a is more efficient than b?

Answer 1

X=10and y=30days, because a is more efficient than b

Answer 2

Answer:

Therefore, b alone takes 30days to complete the entire job.

Step-by-step explanation:

As per the given question:-

-> 'a' and 'b' working together will complete a job in 7.5 (i.e 7 and 1/2) days

-> 'a' works alone for few days and completes half of the job

-> After that, 'b' takes over and alone completes the remaining half of the job and both took 20 days to complete the job

'a' is more efficient than 'b'

We have to find the time taken by 'b' alone to complete the job

a + b one day's work = $\frac{1}{7.5} = \frac{10}{75} = \frac{2}{15}$

Let us consider a works for x days to complete half the job

⇒ a's one day work = $\frac{1}{2x}$

⇒ 'b' takes 20-x days to complete the remaining half of the work.

⇒ b's one day work = $\frac{1}{20*(20-x)}$

$\frac{1}{2x} +\frac{1}{2*(20-x)} =\frac{2}{15}$

⇒$\frac{1}{x} +\frac{1}{20-x} =\frac{4}{5}$

Simplify this,

$\frac{20-x+x}{x*(20-x)} = \frac{4}{15} \\\frac{20}{x*(20-x)} = \frac{4}{15} \\x*(20-x) = \frac{20*15}{4} \\x*(20-x) = 5*15$

Comparing the terms on both sides then x=5

Therefore b's one day work = $\frac{1}{2*15} =\frac{1}{30}$

'b' alone takes 30days to complete the job.