A can do of a piece of work in 32 days, B can do 37% 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 the work, A joined C and both 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?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. .
A can do a piece of work = 32 × 3 = 96 days
B can do a piece of work = 24 × (200/75) = 64 days
C can do a piece of work = 48 × (100/60) = 80 days
Total work = 960 (LCM of 96, 64, 80)
Efficiency of A = 960/96 = 10 work/day
Efficiency of B = 960/64 = 15 work/day
Efficiency of C = 960/80 = 12 work/day
So, (B + C) × x + (A + C) × (x + 8) = 960
⇒ (15 + 12) × x + (10 + 12) × (x + 8) = 960
⇒ 27x + 22(x + 8) = 960
⇒ 27x + 22x + 176 = 960
⇒ 49x = 784
⇒ x = 784/49 = 16
Total work done by C in 3.5x days = 3.5 × 16 × 12 = 672
Required fraction = 672/960 = 7/10
Therefore, C alone can complete 7/10 of the work.