Question

A and B working together can complete a work in 'D' days . Working alone A takes (8+d) days and B takes (18+d) days to complete the same work. A works for 4 days , so the remaining work will be completed by B alone in how many days ?​

Answer 1

The remaining work will be completed by B alone in 24 days .

Step-by-step explanation:

Given as :

A and B working together can complete a work in 'd' days

A alone can work in 8 + d days

So, A's 1 day work = $\dfrac{1}{8+d}$

B alone can work in 18 + d days

So, B's 1 day work = $\dfrac{1}{18+d}$

And

(A + B)'s 1 day work = $\dfrac{1}{d}$

Again

(A + B)'s 1 day work =  A's 1 day work  +  B's 1 day work

i.e  $\dfrac{1}{d}$  = $\dfrac{1}{8+d}$   +  $\dfrac{1}{18+d}$

Or,   $\dfrac{(8+d)(18+d)}{d}$  = 18 + d + 8 + d

Or,   144 + 8 d + 18 d + d²  = d ( 26 + 2 d)

Or,   144 + 26 d + d²  = 26 d + 2 d²

Or,  2 d²  - d² = 144

Or,            d² = 144

∴               d = √144

i.e             d = 12                    .............1

So, A and B together can complete work in d = 12 days

Again

A works for 4 days , so the remaining work will be completed by B alone

So, ∵ A's 1 day work = $\dfrac{1}{8+d}$

∴       A's 4 day work = $\dfrac{1}{8+d}$ × 4  = $\dfrac{4}{8+d}$

Rest of the work is done by B alone

rest of work = 1 - $\dfrac{4}{8+d}$

                    = $\dfrac{8+d-4}{8+d}$

                    = $\dfrac{4+d}{8+d}$

Now,  

∵  $\dfrac{1}{18+d}$  work is done by B in 1 day

∴  $\dfrac{4+d}{8+d}$  work is done by B in  $\dfrac{4+d}{8+d}$  ×$\dfrac{18+d}{1}$    day    

                                              = $\dfrac{(4+d) (18+d)}{(8+d)}$ days

Put the value of d = 12 from eq 1

                                             =  $\dfrac{(4+12) (18+12)}{(8+12)}$days

                                             =  $\dfrac{16\times 30}{20}$ days

                                             = 24 days

So, The remaining work will be completed by B alone in = 24 days

Hence, The remaining work will be completed by B alone in 24 days . Answer

Answer 2

Step-by-step explanation:

(8+12)

(4+12)(18+12)

days

= \dfrac{16\times 30}{20}

20

16×30

days

= 24 days

So, The remaining work will be completed by B alone in = 24 days

Hence, The remaining work will be completed by B alone in 24 days . Answer