Question

A and B can complete a work together in 24 days. If for the last 6 days, A alone does the work, then the work is completed in 26 days. Find the number of days B will take to complete the work alone?

• A. 72 days
• B. 36 days
• C. 67 days
• D. 70 days

Answer 1

The correct option is A

72 days

Let us assume
A's 1-day work = $\frac{1}{A}$
B's 1-day work = $\frac{1}{B}$
(A and B)'s 1-day work together = 1/24
A's 6-day work = $\frac{6}{A}$
Now, for 20 days, A and B work together and for last 6 days, only A works.
Given
$\frac{1}{A}$ + $\frac{1}{B}$ = $\frac{1}{24}$ ___(i)
A's and B's 20-days work + A's 6 days work = 1
20($\frac{1}{A}$ + $\frac{1}{B}$) + $\frac{6}{A}$ = 1
20($\frac{1}{24}$) + $\frac{6}{A}$ = 1
$\frac{6}{A}$ = (1 - $\frac{5}{6}$) = $\frac{1}{6}$
A = 36
From eq. (i)
$\frac{1}{36}$ + $\frac{1}{B}$ = $\frac{1}{24}$
$\frac{1}{B}$ = $\frac{1}{24}$ -$\frac{1}{36}$ = $\frac{1}{72}$

Therefore, B alone will complete the work in 72 days.