A and B can do a job in 25 days and 18 days, respectively. A works alone for 4 days and leaves. The number of days required by B to complete the remaining job is:​

Correct option is A

Given:

A can complete the job in 25 days

rate =$$\frac{1}{25}$$​ job/day.

B can complete the job in 18 days

rate $$=\frac{1}{18}$$​ job/day.

A works alone for 4 days, then leaves.

Find: Days required by B to finish the remaining work.

Formula Used:

Work done = Rate $$\times$$​ Time.

Solution:
Work done by A in 4 days $$=4 \times \frac{1}{25}=\frac{4}{25}$$​​
Remaining work =$$1-\frac{4}{25}=\frac{21}{25}$$​​

Time for B to finish =$$\dfrac{\frac{21}{25}}{\frac{1}{18}}=\frac{21}{25}\times 18=\frac{378}{25}$$ = $$15\frac{3}{25}$$​ days.

Alternate Method:

Take total work = LCM(25,18)=450 units.
A’s rate =450/25=18 units/day

in 4 days does 72 units.
Remaining = 450 - 72 = 378 units.
B’s rate = 450/18 = 25 units/day

​$$\frac{378}{25}=15\frac{3}{25}$$​ days.