Correct Answer - Option 2 : 4
Given:
Babe = 30% of work in 6 days
Tom = 5/6 of work in 25 days
Sam = 40% of work in 20 days
Concept used:
In this type of time and work question, we assume the total work to be done as the LCM of the number of days taken to each of the persons to complete the work.
Formula used :
Total work = Efficiency × Number of days
CALCULATION :
Babe alone can complete whole work in (6/30) × 100 days = 20 days
Tom alone can complete whole work in (25/5) × 6 days = 30 days
Sam alone can complete whole work in (20/40) × 100 days = 50 days
Suppose the total work is (LCM of 20, 30 and 50) i.e., 300 units
One day work by Babe = 300/20 = 15 units
One day work by Tom = 300/30 = 10 units
One day work by Sam = 300/50 = 6 units
According to question –
⇒ \(\left( {15 + 10} \right) \times x + 6 \times \left( {x + 29\frac{1}{3}} \right) = 300\)
⇒ 25x + 6x + 176 = 300
⇒ 31x = 300 – 176
⇒ 31x = 124
⇒ x = 124/31
⇒ x = 4
∴ The value of x is 4.
