# Moderate Time and Work Solved QuestionAptitude Discussion

 Q. A can build up a structure in 8 days and B can break it is 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 structure?
 ✖ A. 10 ✖ B. 9 ✖ C. 12 ✔ D. None

Solution:
Option(D) is correct

A can build the structure in 8 days.

Fraction of structure built in a day by A = $\dfrac{1}{8}$

Similarly, fraction of structure broken by B in a day = $\dfrac{1}{3}$

Amount of work done by A in 4 days = $\dfrac{4}{8}=\dfrac{1}{2}$

Now, both A and B together for 2 days.

So, fraction of structure built in 2 days = $2\left(\dfrac{1}{8}-\dfrac{1}{3}\right)=-\dfrac{5}{12}$

Fraction of structure still to be built = $\dfrac{1}{2}+\dfrac{5}{12}=\dfrac{11}{12}$

If A takes $x$ days to build up the remaining structure, then $\dfrac{x}{8}=\dfrac{11}{12}$

$⇒x$= 22/3 days.

## (2) Comment(s)

TINKU
()

A-8

B-3 LCM OF 8,3=24

TOTAL WORK= 24

A WORKD FOR 4 DAYS WITH EFFICIENCY OF 3 = 12 WORK

24-12=12 WORK REMAINS

NOW A AND B WORKED FOR 2 DAYS

A=3*2=6

B=8*2=16

B-A=10

TOTAL WORK REMAINED = 12+10=22

NOW A WILL COMPLETE IN 22/3DAYS

Sm Mudabbir
()

A will do 6/8 work in 6 days

B will destruct 2/3 in 2 days

now the work A has to do again is 1-(6/8-2/3)=11/12

A will do 11/12 work in 8*(11/12) days=22/3 days