A and B together can finish a piece of work in 10 days B and C together do it in 12 days whereas A a...........

Quant (SSC) Time and work

A and B together can finish a piece of work in 10 days, B and C together do it in 12 days whereas A and C together finish it in 20 days. What is the respective ratio of the number of days taken by A when completing the same work alone to the number of days taken by C when completing the same work alone?

1 : 4

1 : 3

3 : 4

None of these

छोटे Courses बड़े Results

Master Time and work

Prepare through Micro-courses

Try Now

Explanation:

According to the question,
1/A + 1/B = 1/0 ..........i
1/B + 1/C = 1/12 ........II
and 1/C + 1/A = 1/20 .....iii
Adding eqn. (i), (ii) and (iii), we get
2(1/A + 1/B + 1/C) = 1/10 + 1/12 + 1/20
⇒ 1/A + 1/B + 1/C = 7/60 ......iv
Subtracting Eqn. (ii) from Eqn.(iv), we get
1/A = 7/60 - 1/12 = 2/60 = 1/30
Therefore, A will take 30 days to finish the whole work working alone.
Now, Subtracting Eqn. (i) from Eqn.(iv), we get
1/C = 7/60 - 1/10 = 7 - 6/60 = 1/60
Therefore, C will take 60 days to finish the whole work working alone.
∴ Reqd ratio of days = 30 : 60 = 1 : 2