20 men can finish a piece of work in 5 days, whereas it takes 24 women to finish it in 5 days. If 30 men and 12 women undertake to complete the work, how many days will they take to complete it ?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 2.5.
Total work = Efficiency × Time taken
Let the efficiency of 1 man and 1 woman be x and y respectively
Total work done by 20 men in 5 days = 20x × 5 = 100x
Total work done by 24 women in 5 days = 24y × 5 = 120y
According to the question
⇒ 100x = 120y
⇒ x/y = 120/100
⇒ x/y = 6/5
⇒ x : y = 6 : 5
Suppose, x = 6 and y = 5
Total work = 20 × 6 × 5 = 600 units
\Work done by 30 men and 12 women in 1 day = 30 × 6 + 12 × 5 = 180 + 60 = 240 units
15 men and 6 women, complete the whole work in = 600/240 = 2.5 days