Solution:

Ram completes 40% of work in 12 days.

i.e. another 60% of the work has to be completed by Ram and Ravi. They have taken 12 days to complete 60% of the work.

Therefore, Ram and Ravi, working together, would have completed the entire work in (12/60)×100=20 days.

As Ram completes 40% of the work in 12 days, he will take (12/40)×100=30 days to complete the entire work

Working alone, we know Ram takes 30 days to complete the entire work. Let us assume that Ravi takes 'x' days to complete the entire work, if he works alone. And together, they complete the entire work in 20 days.

Therefore, 1/30+1/x=1/20

⇒ 1/x=/1/20–1/30=1/60

Therefore, Ravi will take 60 days to complete the work, if he works alone.

Hence, Ram is 100% more efficient than Ram.

Solution:

In 2 minutes, the taps fill 2(1/12+116) or 5/18of the tank.

Therefore, (13/18)th of the tank is to be filled by the second tap at the rate of

1/18 of the tank per minute.

This will take another 13 minutes.

Solution:

The average cost of production c is a function of a single variable q, the number of workers employed. 

Hence the total cost of production is given by the product c×q=T,say: 

T=c×q=q(q2/3+5q/2−150+75/q).

As, ∂T/∂q=0 

⇒ q=10.

Hence, 10 workers should be employed.

Solution:

Pipe A fills the tank normally in 2 hours. Therefore, it will fill 1/2

 of the tank in an hour.

Let the leak take x hours to empty a full tank when pipe A is shut. Therefore, the leak will empty 

1/4 of the tank in an hour.

The net amount of water that gets filled in the tank in an hour when pipe A is open and when there is a leak =1/2−1/x of the tank. ------- (1)

When there is a leak, the problem states that Pipe A takes two and a half hours to fill the tank. i.e. 5/2 hours. 

Therefore, in an hour,(5/2)th of the tank gets filled. --------- (2)

Equating (1) and (2), we get  1/2−1/x=2/5

⇒ 1/x=1/2−2/5=110

 ⇒ x = 10 hours.

The problem can also be done mentally as follows.

Pipe A takes 2 hours to fill the tank. Therefore, it fills half the tank in an hour or 50% of the tank in an hour.

When there is a leak it takes 2 hours 30 minutes for the tank to fill. i.e 5/2

hours to fill the tank or (2/5)th or 40% of the tank gets filled.

On account of the leak, (50−40)%=10% of the water gets wasted every hour. Therefore, the leak will take 10 hours to drain a full tank.

Solution:

In 1 day Pankaj and Bharti together produce =1/15+1/12=3/20 units

In 20 days, together they can produce (3/20)20=3 units.

From which they can fetch Rs 270

Efficiency of Bharti/Efficiency of pankaj=15/12=5/4

⇒ Share of Bharti is (5/9)270= Rs 150