Question

A can build up a wall in 8 days while B can break it in 3 days. A has worked for 4 days and then B joined to work with A for another 2 days only. In how many days will A alone build up the remaining part of the wall?

• A. 7 1/3 days
• B. 8 2/5 days
• C. 9 1/5 days
• D. 5 1/2 days

Answer 1

Answer:

A. 7 1/3 days

A’s 1-day work = $( \frac{1}{8} )$
B’s 1-day work (destruction) = $( -\frac{1}{3} )$

Work done by A in 4 days

$4 \times \frac{1}{8} = \frac{1}{2}$

So, half the wall is completed.

Remaining work = $( \frac{1}{2} )$

Work when A and B work together for 2 days

Net 1-day work of A + B:

$\frac{1}{8} - \frac{1}{3}$

LCM = 24:

$\frac{3 - 8}{24} = -\frac{5}{24}$

So together they are destroying work.

Work in 2 days:

$2 \times \left(-\frac{5}{24}\right) = -\frac{5}{12}$

So instead of completing, they reduce the completed work.

Work after 6 days total

Initial completed work = $( \frac{1}{2} )$

Loss due to A + B working = $( \frac{5}{12} )$

$\frac{1}{2} - \frac{5}{12}$

LCM = 12:

$\frac{6 - 5}{12} = \frac{1}{12}$

So remaining work = $( \frac{11}{12} )$

A alone completes remaining work

A’s rate = ( \frac{1}{8} )

Time:

$\frac{11/12}{1/8} = \frac{11}{12} \times 8 = \frac{88}{12} = \frac{22}{3}$

Convert to mixed fraction

$\frac{22}{3} = 7\frac{1}{3}$

Final Answer

$\boxed{7\frac{1}{3} \text{ days}}$