A can build up a structure in 8 days and B can break it is 3 days.

Question

A can build up a structure in 8 days and B can break it is 3 days. A worked for 4 days and then is joined by B for two days. For these two days A is building and B is breaking. In how many days after that will A alone build up the remaining part of the structure?

A. 12

B. 11

C. 9

D. 22/3

E. 7

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A. 12

B. 11

C. 9

D. 22/3

E. 7

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Archit3110 · Answer

Rate of A - 1/8 and that of B 1/3
four days work done by A ; 4* 1/8 ; 1/2
two days work combined
2 * ( 1/8 -1/3 ) = -10/24 ;

net work done
1/2 -5/12; 1/12 
work left 11/12
A will take
11/12 * 8 = x
x = 22/3 option D

Abhishek009 · Answer

Let total work be 24 units

So, Efficiency of A = +3 units/day & Efficiency of B = -8 units/day

Work done by A in 4 days is 12 units, work left is 12 units.

Work done by A & B in 2 days is (+3 -8 )*2 = -10 units, work done will be 2 units (12 - 10), work left is 22 units (24 - 2)

Time required by A to complete the work will be (D) 22/3, Answer must be (D)

ScottTargetTestPrep · Answer

Solution:

The amount built in the first 4 days is 1/8 x 4 = 1/2.

The amount breaking in the next two days is:

(1/3 - 1/8) x 2 = (8/24 - 3/24) x 2 = 5/24 x 2 = 10/24 = 5/12

Thus, the amount now built is:

1/2 - 5/12 = 6/12 - 5/12 = 1/12.

To build the remaining 11/12, it will the following number of days:

(11/12)/(1/8) = 88/12 = 22/3 days.

Answer: D

$!vakumar.m · Answer

A can build up a structure in 8 days and B can break it is 3 days. A worked for 4 days and then is joined by B for two days. For these two days A is building and B is breaking. In how many days after that will A alone build up the remaining part of the structure?
A works for 4 days and completes 1/2 work
in next 2 days A does 1/4 work and B breaks 2/3 work
After 6 days, in effect we have (1/2 + 1/4 - 2/3) = 1/12 work
So, A has to do the balance of 11/12 work and to complete that he needs 8*11/12 = 22/3 days

Answer D

Gauravji21 · Answer

Let the work done be 1 unit. Work Done = Time Taken × Rate of Work.

A can build up a structure in 8 days and B can break it is 3 days.
A's rate of work = 1/ 8, B's rate of work= (-)1/3

Work done by A in 6 days (4 days alone and 2 days along with B) = 6 * (1/8) = 3 / 4
Work done by B in 2 days when he was with A = (-) 2* 1/3

Net work done in 6 days = 3/4 - 2/3 = 1/12
Pending work = 1 - 1/12 = 11 /12

Pending Work for A = Time Required × A's Rate of Work. 
11/12 = Time required x 1/8
=> Time required = 11 * 8 /12 = 22 / 3
Answer D

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A can build up a structure in 8 days and B can break it is 3 days.

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A can build up a structure in 8 days and B can break it is 3 days.

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