The time taken by 4 men to complete a job is double the time taken by 5 children to complete the same job. Each man is twice as fast as a woman. How long will 12 men, 10 children and 8 women take to complete a job. (Given that a child would finish the job in 20 days.)
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 1 day
|
Understanding |
Application |
|
Suppose the efficiencies of a man, a woman, and a child are M, W, and C. The time taken by 4 men to complete a job is double the time taken by 5 children to complete the same job. Each man is twice as fast as a woman. |
So, 4M × 2 = 5C ⇒ M : C = 5 : 8 And M : W = 2 : 1 So, M : W : C = 10 : 5 : 16 So, M = 5C/8 and W = 5C/16 |
|
A child would finish the job in 20 days. |
So, Total work = 20C |
|
Suppose 12 men, 10 children, and 8 women take to x days to complete the job. |
So, (12M + 10C + 8W) × x = 20C ⇒ (12 × 5C/8 + 10C + 8 × 5C/16) × x = 20C ⇒ (7.5C + 10C + 2.5C) × x = 20C ⇒ x = 1 Hence, Required time = 1 day |