# Time and Work Problems (Efficiency Questions)

In this post we will discuss Time and Work efficiency based questions.
The questions basically discuss about the efficiency about different workers involved in the work. Some of the questions may be tricky for you if you understand the concept you won’t face any difficulty in the examination.

Question 01

A works twice as fast as B. If B can complete a work in 12 days independently, the number of days in which A and B can together finish the work is?

B alone completes the work in 12 days
so, B’s 1 day work = 1/12

As A is twice as fast as B, it will completes the work in 6 days
Thus, A’s 1 day work = 1/6

Therefore, (A and B)’s 1 day work = 1/12 + 1/6 = 3/12 = 1/4 days

Thus, A and B can together finish the work in 4 days.

Question 02

A is 30% more efficient than B. How much time will they, working together, take to complete a job which A alone could have done in 23 days?

Ratios of time taken by A and B = 100:130 = 10:13

Suppose B takes x days to complete the work.

Then, 10/13= 23/x

10x = 13 × 23

x = 299/10

A’s 1 day work = 1/23 and B’s 1 day work = 10/299

Therefore, (A + B)’s 1 day work = 1/23 + 10/299 = 23/299 = 1/13

Thus, A and B together will complete the work in 13 days.

Question 03

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?

Sol: Let the total work be W.

Let the speed of A be x work/day.
Let the speed of B be y work/day.

Two workers A and B working together completed a job in 5 days.

Therefore, W / (x+y)= 5 ;
W = 5x + 5y……………. (i)

If A worked twice as efficiently as he actually did and B worked 1/3 as efficiently as he actually did the work could have been completed in 3 days.

Therefore, W=6x+y
multiplying by 5 each side we get;
5W = 30x + 5y …………………………… (ii)

On Solving eq (i) and (ii);
W/x=25/4 Therefore, A alone could complete the work in 25/4 (04) A is twice as good a workman as B and B is twice as good a workman as C. If A and B can together finish a piece of work in 4 days, then C can do it by himself in

A completes the work in = x days,
B completes the work in = 2x days,
C completes the work in = 4x days

A & B finish the work in 4 days
1/x + 2/2x = ¼

x = 6

So, C will complete the work in ( 4 × 6 ) = 24 days

(05) A man and a woman working together can do a certain work in 18 days. Their skills in doing the work are in the ratio 3 : 2. How many days will the woman take to finish the work alone?

Man : Woman = Efficiency is 3 : 2.

One day’s work of a man and a woman = ( 3 + 2 ) = 5 units

Total work = 18 × 5 = 90 units

A woman can complete the whole work in 90 / 2 = 45 days