A person employed a group of 20 men for a construction job. These 20 men working 8 hours a day can complete the job in 28 days. The work started on time but after 18 days, it was observed that two thirds of the work was still pending. To avoid penalty and complete the work on time, the employer has to employ more men and also increase the working hours to 9 hours a day. Find the additional number of men employed if the efficiency of all men is same.
Answers
Answer:
No. of men, M1 = 20
No. of hours per day, H1 = 8 hrs and H2 = 9 hrs
Since the 20 men have worked for D1 = 18 days only, so let the no. of men working after 18 days i.e., for D2 = 28-18 = 10 days be “x”.
We are given that for the next 10 days they have to complete 2/3rd of the work, therefore, in first 18 days, they have completed (1 - 2/3) = 1/3rd of work.
Also, the efficiency of all men are same, therefore, E1 = E2 = Efficiency of each man
Let the total work be of 1 unit as a whole.
∴ Work done in first 18 days by 20 men for 8 hrs a day, W1 = (1/3) * 1 = 1/3 unit
And,
Work done in next 10 days by (x + 20) men for 9 hrs a day, W2 = (2/3) * 1 = 2/3 unit
Now, by using the formula below, we get the no. of additional men to be employed,
[M1 * D1 * H1 * E1] / W1 = [M2 * D2 * H2 * E2] / W2
⇒ [20 * 18 * 8 * E1] / 1/3 = [(x+20) * 10 * 9 * E2] / 2/3
⇒ 2880 * 2 = (x+20) * 90
⇒ 64 = x + 20
⇒ x = 44 men
Thus, the additional number of men required to be employed to complete the work and avoid any penalty is 44.