Question : A can do $\frac{1}{3}$rd of a piece of work in 32 days, B can do $37 \frac{1}{2}$% of the same work in 24 days, while C can do 60% of the same work in 48 days. B and C together started and worked for x days. After x days, B left and A joined C and together, completed the remaining work in (x + 8) days. If the ratio of the work done by (B + C) together to the work done by (A + C) together is 9 : 11, then what fraction of the same work can be completed by C alone in 3.5x days?
Option 1: $\frac{18}{25}$
Option 2: $\frac{4}{5}$
Option 3: $\frac{7}{10}$
Option 4: $\frac{3}{4}$
Correct Answer: $\frac{7}{10}$
Solution :
Given: A can do $\frac{1}{3}$ of a task in 32 days.
Total work done = Number of days × Efficiency
So, A can complete the task in 32 × 3 = 96 days
B can do $37 \frac{1}{2}$% of the same task in 24 days,
So, B can complete the task in $24 × \frac{200}{75} = 64$ days
C can do 60% of the same task in 48 days.
So, C can complete the task in $48 × \frac{100}{60} = 80$ days
Total work is LCM of (96, 64, and 80) = 960 units
Efficiency of A is $\frac{960}{96} =10$ units/day
Efficiency of B is $\frac{960}{64} = 15$ units/day
Efficiency of C is $\frac{960}{80} = 12$ units/day
Work done by (B + C) in x days is (15 + 12)x = 27x
The remaining work done by (A + C) in (x + 8) days is (10 + 12)(x + 8) = 22x + 176
According to the question,
So, 27x + 22x + 176 = 960
$\therefore$ x = 16
So, the fraction of the task that C can do alone in 3.5x days is $\frac{3.5×16×12}{960}=\frac{7}{10}$
Hence, the correct answer is $\frac{7}{10}$.
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