Question

a can do a work in 45 days he worked at it for 15 days and then B alone finish the remaining work in 24 days find the time taken to complete 80% of the work if they work together​

Answer 1

The time taken to complete 80% of the work if A & B work together is 16 days.

Step-by-step explanation:

A alone can do a work in 45 days

So, work done by A in 15 days = $\frac{15}{45}$  = $\frac{1}{3}$

∴ Remaining fraction of work that is done by B alone = 1 - $\frac{1}{3}$ = $\frac{2}{3}$ ← in 24 days

∴ The whole work will be done by B alone in = 24 × $\frac{3}{2}$ = 36 days

Now,  

Work done by A in 1 day = $\frac{1}{45}$

Work done by B in 1 day =   $\frac{1}{36}$

∴ Work done by A and B together in 1 day is given by,

=   $\frac{1}{45} + \frac{1}{36}$

=   $\frac{5+4}{180}$

=   $\frac{9}{180}$

=   $\frac{1}{20}$

If, 1 whole work is done by A and B together in 20 days

Then, 80% of the work will be done in = 20 * $\frac{4}{5}$  = 16 days

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Answer 2

Time taken to complete 80% of the work when A and B works together is 16 days

Step-by-step explanation:

Given as :

A can do a work in 45 days

A's 1 day work = $\dfrac{1}{45}$

So, work done by A in 15 days = 15 × $\dfrac{1}{45}$

                                                   = $\dfrac{1}{3}$

Remaining work = 1 - $\dfrac{1}{3}$

i.e  Remaining work = $\dfrac{3-1}{3}$  = $\dfrac{2}{3}$

Now,  B alone finishes the remaining work in 24 days

So, Remaining Work done by B in  24 days = 24 × $\dfrac{3}{2}$

i.e                                                                     = 12 × 3

∴                                                                       = 36

So B's 1 day work  = $\dfrac{1}{36}$

So, The (A + B) 's 1 day work = A's 1 day work + B's 1 day work

i.e                                            = $\dfrac{1}{45}$  +  $\dfrac{1}{36}$

                                               = $\dfrac{4+5}{180}$

                                               = $\dfrac{9}{180}$ = $\dfrac{1}{20}$

i.e (A + B)  together 1 day work  = $\dfrac{1}{20}$

∴  Work completed by (A + B)  working together is in = 20 days

So, Time taken to complete 80% of the work = 80% × 20 days

                                                                           = $\dfrac{80}{100}$ × 20 days

                                                                           = 16 days

So,  Time taken to complete 80% of the work when A and B works together = 16 days

Hence, Time taken to complete 80% of the work when A and B works together is 16 days   Answer