A can do 1/5 of a piece of work in 20 days, B can do 30% of the same work in 36 days, while 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?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 57/100.
Givent that
A can do a piece of work in = 20 × 5 days = 100 days
B can do the same work in = 36 × 10/3 day = 120 days
C can do the same work in =160 × 10/8 days = 200 days
Total work = LCM (100, 120, 200) = 600
The efficiency of A = 600/100 = 6
The efficiency of B = 600/120 = 5
The efficiency of C = 600/200 = 3
As we know,
Work = time × efficiency
According to the question
⇒ (B + C) × x + (A + C) × (x - 41) = 600
⇒ ( 5 + 3)x + (6 + 3) × (x - 41) = 600
⇒ 8x + 9x - 369 = 600
⇒ 17x = 969
⇒ x = 57 days
Hence, C alone do the fraction of work in 2x days = 2× 57 × 3/600 = 57/100