Time and Work
Aptitude

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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

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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