Time & Work Set 7 : How many Days required ?
1. A does a work in 6 days. B does half of the work in 6 days. How many days will A and B take together to finish the whole work ?
Soln:
A’s 1-day work = 1/6
B does half work in 6 days → full work in 12 days
So, B’s 1-day work = 1/12
Together in 1 day: 1/6 + 1/12 = 1/4
If they do 1/4 work in 1 day,
they will do full work in 4 days.
Ans: 4 days
2. One pipe fills a tank in 12 minutes. Another pipe drains water at 14 liters per minute. When both pipes are opened together, the empty tank fills in 96 minutes. Find the capacity of the tank.
Soln
First think: The inlet fills the tank in 12 minutes, and with the outlet open, the tank fills in 96 minutes.
Compare the fast time (12 min) with the slow time (96 min). The difference shows how much water the outlet removes.
Multiply the difference in time by the outlet’s speed.
o Difference in time = 96 − 12 = 84 minutes
o Outlet removes = 14 liters per minute
Now multiply: 84 × 14 = 1176 liters removed
This removed water equals the amount already filled by the inlet over those extra minutes.
The inlet fills 1/12 of the tank per minute. So in 84 minutes, it fills: 84/12 = 7 tanks
Therefore 1176 liters = 7 tanks
Tank capacity = 1176 ÷ 7 = 192 liters
Ans: 192 liters
3. A car wheel rotates 90 times per minute. How many degrees does it rotate in 1 second ?
Soln:
1 minute = 60 seconds
The wheel makes 90 rotations in 60 seconds.
So, in 1 second it makes: 90/60 = 1.5 rotations
One full rotation = 360°
Therefore, in 1.5 rotations, it turns: 1.5×360=540∘
Ans: 540°
4. 10 men working 6 hours per day can finish a work in 14 days. How many hours per day must 12 men work to finish the same work in 10 days ?
Soln
Calculate total man-hours required for the work
Total work = men × days × hours/day
= 10 × 14 × 6
= 840 man - hours
Let required hours per day for 12 men = x
They must complete 840 man-hours in 10 days: 12 × 10 × x = 840
Solve for x
120x = 840
X = 840/120
X = 7
Ans: 12 men must work 7 hours per day.