Rate & work:-"A" alone can complete a work in

[vinni.k]

"A" alone can complete a work in 16 days and "B" alone in 12 days. Starting with "A", they work on alternate days. The total work will be completed in:

(a). 12 days
(b). 13 days
(c). 13(5/7) days
(d). 13(3/4) days
(e). none

OA is D

[ganeshrkamath]

"A" alone can complete a work in 16 days and "B" alone in 12 days. Starting with "A", they work on alternate days. The total work will be completed in:

(a). 12 days
(b). 13 days
(c). 13(5/7) days
(d). 13(3/4) days
(e). none

OA is D

A's rate of work = 1/16
B's rate of work = 1/12
In 2 days, A and B complete (1/16 + 1/12) = (3+4)/48 = 7/48 of the work
In 6*2 = 12 days, they complete (7*6)/48 = 42/48 of the work
In 13 days, they complete 42/48 + 1/16 = 45/48 of the work
Remaining work = 3/48
B can do 1/12 = 4/48
So it takes 13 3/4 or 13.75 days to complete.

Choose D

Cheers

[GMATGuruNY]

"A" alone can complete a work in 16 days and "B" alone in 12 days. Starting with "A", they work on alternate days. The total work will be completed in:

(a). 12 days
(b). 13 days
(c). 13(5/7) days
(d). 13(3/4) days
(e). none

OA is D

Let the job = the LCM of 16 and 12 = 48 units.

A's rate = w/t = 48/16 = 3 units per day.
B's rate = w/t = 48/12 = 4 units per day.
When A and B alternate, the amount of work produced every 2 days = 3+4 = 7 units.
Thus, after 2*6 = 12 days, the amount of work produced = 7*6 = 42 units.

Amount of work remaining after 12 days = 48-42 = 6 units.
On the 13th day, A produces 3 more units.
Amount of work remaining after 13 days = 6-3 = 3 units.
Time for B to complete the remaining 3 units = w/r = 3/4 days.
Total time = 13 + 3/4 = 13.75 days.

The correct answer is D.

[vinni.k]

Thanks

Regards
Vinni