A can finish as much work in 6 days as C can in 8 days. B can finish as much work in 6 days as C can in 4 days. How much time will B require to finish a work if A takes 54 days to finish it?
- A118 days
- B128 days
- C100 days
- D108 days
Solution & Step-by-step Explanation
Let the work efficiencies (work done per day) of A,B, and C be denoted by E
A
,E
B
, and E
C
respectively.
From the first statement:
Work done by A in 6 days=Work done by C in 8 days
6×E
A
=8×E
C
⟹
E
C
E
A
=
6
8
=
3
4
From the second statement:
Work done by B in 6 days=Work done by C in 4 days
6×E
B
=4×E
C
⟹
E
C
E
B
=
6
4
=
3
2
From these ratios, we can express the efficiencies of A and B relative to C:
E
A
=4k,E
B
=2k,E
C
=3k
Given that A takes 54 days to finish the work:
Total Work=Efficiency of A×Time taken by A
Total Work=4k×54=216k
Now, we calculate the time required by B to finish the same work:
Time taken by B=
Efficiency of B
Total Work
=
2k
216k
=108 days
A
,E
B
, and E
C
respectively.
From the first statement:
Work done by A in 6 days=Work done by C in 8 days
6×E
A
=8×E
C
⟹
E
C
E
A
=
6
8
=
3
4
From the second statement:
Work done by B in 6 days=Work done by C in 4 days
6×E
B
=4×E
C
⟹
E
C
E
B
=
6
4
=
3
2
From these ratios, we can express the efficiencies of A and B relative to C:
E
A
=4k,E
B
=2k,E
C
=3k
Given that A takes 54 days to finish the work:
Total Work=Efficiency of A×Time taken by A
Total Work=4k×54=216k
Now, we calculate the time required by B to finish the same work:
Time taken by B=
Efficiency of B
Total Work
=
2k
216k
=108 days