A and B can do a task in 15 and 20 days respectively. With the help of C, they finish the work in 8 days. In how much time can C alone do a work twice as large as the first one?
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- A and B can do a task in 15 and 20 days respectively.
- With the help of C, they finish the work in 8 days.
Let C takes x days to complete their work.
One day work of A, B and C
→ 1/15 , 1/20 and 1/x
→ 1/15 + 1/20 + 1/x = 1/8
→ 4+3/60 + 1/x = 1/8
→ 7/60 + 1/x = 1/8
→ 7x+60/60x = 1/8
→ 7x+60/15x = 1/2
→ 14x+120 = 15x
→ 15x - 14x = 120
→ x = 120
Afterall, C alone takes 120 days to complete work.
»› Work ratio of A and C are,
→ 15/120
→ 1/8 = 1:8
»› Finally, If C wanna do work twice as large as A then..,
→ 15/120 × 2/2
→ 30/240
Hence,
C alone can take 240 days to complete work which is twice as large as work of A.
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