Work and Time Problems with Solutions

Q1. Ajay can do a piece of work in 25 days and Sanjay can finish it in 20 days. They work together for 5 days and then Ajay goes away. In how many days will Sanjay finish the remaining work?

Answer: As we have done in our Previous Example, we consider that Ajay does 25 units of work in 25 days and Sanjay does 20 units of work in 20 days.

Since efficiency of Sanjay is 5, 
so the remaining work will done in 55/5 = 11 days.

Q2. It is given that 16 men working 18 hours a days can build a wall 36 m long, 4 m broad and 24 m high in 20 days. How many men will be required to build a wall 64 m long, 6 m broad and 18 m high working 12 hour a day in 16 days?

Answer: There is a technique to solve this type of work and time problems quickly. The short trick to solve this problem is

M₁D₁T₁W₂ = M₂D₂T₂W₁

By applying this rule we get

16*18*20*(64*6*18) = M₂*12*16*(36*4*24)

M₂ = 60

Q3. P can do a piece of work in 12 days, while Q alone can finish it in 8 days. With the help of R they can finish the work in 4 days. How long will R take to finish the work alone?

Answer: As we have done previously, here also we consider that P does 12 units of work, Q does 8 units of work and P,Q,R all together do 4 units of work. (1 unit/days)

So taking LCM of 12, 8, 4 we get 24 as total units of work. Now,

So we have seen in the picture that R’s efficiency is 1, i.e. R can do 1 unit of work in one day. As we found that the total work is 24 units,

so to do the whole work alone 

R will take 24/1 = 24 days.

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