Time and Work Relation between Efficiency

Relation between Efficiency

In this case the efficiency of different persons are different but when they work in a group, so the efficiency of the group is required to know the time taken. For example 3 men can do a work in 4 days while 12 boys can do the same work in 3 days. It means we need 3 x 4 = 12 man – days i.e., 12 men can finish the job in 1 day.

Similarly we need 12 x 3 = 36 boys days i.e., 36 boys can finish the same job in 1 day.

Here we can see that to finish the work in only 1 day 12 men are needed while 36 boys are needed. Thus we can conclude that work of 12 men is equal to the work of 36 boys. Therefore efficiency of 12 men is equal to 36 boys i.e., we can say the efficiency of 1 man is equal to 3 boys. Thus a man is thrice efficient as a boy or we can say that a man is two times more efficient than a boy.

Problem:

6 boys and 8 women finish a job in 6 days and 14 boys and 10 women finish the same job in 4 days. In how many days working together 1 boy and 1 woman can finish the work?

Solution:

In this kind of question we find the work force required to complete the work in 1 day (or given unit of time) then we equate the work force to find the relationship between the efficiencies (or work rate) between the different workers.

Therefore 6B + 8W = 6 days

= 6 (6B + 8W) = 1 day (Inversely proportional)

= 36B + 48W = 1

Again 14B + 10 W = 4 days

56B +40W =1

So, here it is clear that either we employ 36B and 48W to finish the work in 1 day or 56B and 40W to finish the same job in 1 day. Thus we can say

= 36B+48W = 56B+40W

20B =8W

W = 2.5B

Thus a woman is 2.5 times as efficient as a boy

Now since 36B + 48W =1

36B +48 X (2.5B) =1

156B =1

i.e. to finish the job in 1 day 156 boys are required or the amount of work is 156 boys-days

again 1W+1B = 2.5B + 1B = 3.5B

Now. Since 156 boys can finish the job in 1 day

So 1 boy can finish the job in 1 X 156 days

Therefore 3.5boys can finish the job in 1 X156/3.5 = 44 4/7 days

6 men and 8 women can do a job in 10 days. In how many days can men and 9 women do the same job?

Solution:

Since we don’t know the relation between work rate ( or efficiency) between a man and that of a women so we cant find the required number of days.

6 men and 8 women can do a job in 10 days. In how many days can 3 men and 4 women finish the same job working together?

Solution:

Notice here we don’t know the relation of efficiencies but we can solve the problem due to clear relation between the work force.

Since   6M + 8W = 10 days

            2(3M + 4W) = 10 days

= (3M+4W) = 20 days

Since, the work force has become half of the original force so number of days must be double

Thus required number of days = 20