A is 1.5 times efficient as B therefore takes 8 days less than B to complete a work. If A and B work on alternate days and A works on first day, then in how many days the work will be completed?
A is 1.5 times efficient as B therefore takes 8 days less than B to complete a work. If A and B work on alternate days and A works on first day, then in how many days the work will be completed?
1). 17
2). 19
3). 19.5
4). 21
1 answers
Let the days taken by B to complete the work = c days
So, days taken by A to complete the work = c - 8 days
Now, it is given that A is 1.5 times efficient as B
⇒ c = 1.5 x (c – 8)
⇒ 0.5c = 12
⇒ c = 24
Work done by B in 1 day = 1/24
Work done by A in 1 day = 1/16
Hence, the series becomes: 1/16 + 1/24 + 1/16 + ……. = 1
⇒ Work done in 2 consecutive days = 1/24 + 1/16 = 5/48 = 1/9.6
⇒ Work done in 18 consecutive days = 9/9.6
⇒ Work left after 18 days = 1 – (9/9.6) = 0.6/9.6 = 1/16
Since A will work on the 19th day and will complete 1/16 of the work
∴ Total days = 18 + 1 = 19