Correct Option: A
Let A and C complete the work in y days
| (A + B)’s 1 day’s work = | 1 | |
8 |
| (B + C)’s 1 day’s work = | 1 | |
12 |
| (C + A)’s 1 day’s work = | 1 | |
y |
| Then (A + B + B + C + C + A)’s 1 day’s work = | 1 | + | 1 | + | 1 |
8 | 12 | y |
| 2(A + B + C)’s 1 day’s work = | 3y + 2y + 24 | |
24y |
| (A + B + C)’s 1 day’s work = | 5y + 24 | |
24y × 2 |
According to the question,
| (A + B + C)’s 1 day’s work = | 1 | |
6 |
⇒ 30y + 144 = 48y
Second method to solve this question ,Let the time taken by A and C be y days
Here , p = 8 , q = 12 , r = y
| Time taken = | 2pqr | |
pq + qr + rp |
| ⇒ Total time taken = | 2 × 8 × 12 × y | |
8 × 12 + 12 × y + 8 × y |
⇒ 576 + 120y = 192y
⇒ 72y = 576
⇒ y = 8
Time taken by A and C is 8 days.
