In a group. X men work an efficiency E, men work with efficiency 4E. The group complete Job- A in 13 days in which total effort required was 10001E man-days. In another group X men work with efficiency 2E and Y man work with efficiency 5E. This group completed job-B in 16 days and total effort was 1793E man-days. How long will (4X+3) men working at efficiency E and (Y+9) me working at efficiency 2E take to complete both job A and Job-B?

 

In a group. X men work an efficiency E, men work with efficiency 4E. The group complete Job- A in 13 days in which total effort required was 1001E man-days. In another group X men work with efficiency 2E and Y man work with efficiency 5E. This group completed job-B in 16 days and total effort was 1793E man-days. How long will (4X+3) men working at efficiency E and (Y+9) me working at efficiency 2E take to complete both job A and Job-B?

A.    21 days

B.    26 days

C.    15 days

D.    11 days

 

A. 21

 

 

 

 

Man-days required to complete a job= m*d*e, where m= number of men, d=days and e= efficiency.

Hence for Job A, man-days required= x*13*E+y*13*4E=1001E

 

Thus 13x*E+52y*E=1001E

For Job B, man-days required= x*2E*16+y*5E*16=1792E. Thus 32x+80y=1792.

 

Solving for x and y, we have x=21 and y=14.

Now 4x+3=4*21+3=87 and y+9=14+9=23.Total man-days required to complete jobs A and B together=1001E+1792E=2793E man-days.

 

2793E=87*d*E+23*d*2E

Thus d= 2793/133=21days.

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