Question : A can-do $\frac{1}{5}$ of a piece of work in 20 days, B can do 30% of the same work in 36 days, and C can do 80% of the same work in 160 days. B and C together started and worked for x days. After x days B left the work, and A joined C and both completed the remaining work in (x - 41) days. If the ratio between the work done by (B + C) together to the work done by (A + C) together is 19: 6, then what fraction of the same work can be completed by C alone in 2x days?
Option 1: $\frac{57}{100}$
Option 2: $\frac{13}{25}$
Option 3: $\frac{19}{25}$
Option 4: $\frac{6}{25}$
Correct Answer: $\frac{57}{100}$
Solution :
A can-do $\frac{1}{5}$ of a piece of work in 20 days
⇒ A can finish complete work in 100 days.
B can complete 30% of the work in 36 days
⇒ B can finish complete work in 120 days.
C can complete 80% of the work in 160 days
⇒ C can finish the complete work in 200 days.
B and C together started and worked for x days
⇒ efficiency of B and C = $\frac{1}{120}+\frac{1}{200}$
= $\frac{8}{600}$
In x days, work done by B and C = $\frac{8}{600}$x
A and C together worked for (x - 41) days
⇒ Efficiencies of A and C = $\frac{1}{100}+\frac{1}{200}$ = $\frac{3}{200}$
In (x – 41) days, work done by A and C = $\frac{3}{200}$(x - 41)
According to the question
$\frac{8}{600}$x: $\frac{3}{200}$(x - 41) = 19: 6
⇒ $x$ = $\frac{57 × 41}{41}$ = 57
Now,
The same work be completed by C alone in 2x days
= 2 × 57 × $\frac{1}{200}$
= $\frac{57}{100}$
Hence, the correct answer is $\frac{57}{100}$.
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