Question : A and B can do a work in $26 \frac{2}{3}$ days. B and C together can complete the same work in 48 days, while A and C together can complete the same work in 30 days. How long (in days) will A alone take to complete 60% of the work?
Option 1: 20
Option 2: 32
Option 3: 24
Option 4: 36
Correct Answer: 24
Solution :
Use :
Work = Efficiency × Time
According to the question
LCM of $\frac{80}{3}$, 48 and 30 = 720
⇒ Efficiency of A and B = 720 × $\frac{3}{80}$ = 27
⇒ Efficiency of B and C = $\frac{720}{48}$ = 15
⇒ Efficiency of A and C = $\frac{720}{30}$ = 24
Total Time Taken by A, B, and C to Complete Work = $\frac{27+15+24}{2}=\frac{64}{2}= 32$ days
Now,
Time Taken by A, B, and C to complete the 60 % of the work
= $\frac{\text{60% of the total work}}{\text{Time}}$
= $\frac{720}{33 – 15}$ × $\frac{60}{100}$
= $\frac{720}{18}$ × $\frac{3}{5}$
= $24$ days
Hence, the correct answer is 24.
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