1. X can do a piece of work in 40 days. He works at it for 8 days and then Y finished it in 16 days. How long will they together take to complete the work?

A. 13 1/3 days B. 15 days C. 20 days D. 56 days

Answer Answer: Option A Explanation: Work done by X in 8 days = (1/40*8) = 1/5. Remaining work = (1- 1/5) = 4/5.
Now, 4/5 work is done by Y in 16 days.
whole work will be done by Y in (16*5/4) = 20 days.
therefore X's 1 day's work = 1/40, Y's 1 day's work = 1/20.
(X+Y)'s 1 day's work = (1/40+ 1/20) = 3/40.
Hence, X and Y will together complete the work in 40/3 = 13 1/3 days.

2. X can do 1/4 of a work in 10 days, Y can do 40% of the work in 40 days and Z can do 1/3 of the work in 13 days. Who will complete the work first?

A. X B. Y C. Z D. X and Z both

Answer Answer: Option C Explanation: Whole work will be done by X in (10*4) = 40 days.
Whole work will be done by Y in (40*100/40) = 100 days.
Whole work will be done by Z in (13*3) = 39 days.
Therefore Z will complete the work first.

3. X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of the work. How long did the work last?

A. 6 days B. 10 days C. 15 days D. 20 days

Answer Answer: Option B Explanation: Work done by X in 4 days = (1/20*4) =1/5. Remaining work = (1- 1/5) = 4/5.
(X+Y)'s 1 day's work = (1/20+1/12) = 8/60 = 2/15.
Now, 2/15 work is done by X and Y in 1 day.
So, 4/5 work will be done by X and Y in (15/2*4/5) = 6 days.
Hence, total time taken = (6+4) days = 10 days.

4. Worker A takes 8 Hours to do a job. Worker B Takes 10 Hours to do the same job. How long should it take both A & B working together but independently to do the Same Job?

A. 32/9 B. 40/9 C. 35/8 D. 30/5

Answer Answer: Option B Explanation: A's 1 Hour work=1/8, B's 1hour work =1/10
(A+B)'s 1 hour work =(1/8+1/10)=9/40.
Both A & B Complete the work in 40/9 days

5. Two workers A and B working together completed a job in 5 days. If A worked twice as efficiently as he actually did and B worked 1/3 as efficiently as he actually did, the work would have been completed in 3 days. A alone could complete the work in?

A. 5 1/4 days B. 6 1/4 days C. 7 1/2 days D. none of these

Answer Answer: Option B Explanation: Let A's 1 day's work = x and B's 1 day's work = y.
Then, x+ y = 1/5 and 2x + 1/3y = 1/3.
solving, we get : x = 4/25 and y = 1/25.
therefore A's 1 day's work = 4/25.
so, A alone could complete the work in 25/4 = 6 1/4 days.