## Solved Time & Work Problems For HCL Aptitude Tests

Below are three problems on time and work which you can expect in HCL and other companies placement tests.

**Question 1**

In a factory, there are two machines A and B. A machine can produce 1000 watts power in 5 hours and by running both the machines together can produce same watts power in 3 hours. Find the time taken by B machine alone to produce same watts of power.

a) 5 hrs b) 7 hrs & 30 mins c) 6 hrs d) 6 hrs & 30 mins

**Answer :**b) 7 hrs & 30 mins

Solution :

A type machine can produce 1000 watts power in 5 hours.

Then A's 1 hour work = 1/5.

Both A and B can produce in 3 hours.

And 1 hour work of (A + B)'s = 1/3.

B's 1 hour work = 1/3 = 1/5 = 2/15.

Therefore, machine B can produce 1000 watts power in 15/2 hours.

i.e., 15/2 hours = 7.5 hours = 7 hours and 30 minutes.

Then A's 1 hour work = 1/5.

Both A and B can produce in 3 hours.

And 1 hour work of (A + B)'s = 1/3.

B's 1 hour work = 1/3 = 1/5 = 2/15.

Therefore, machine B can produce 1000 watts power in 15/2 hours.

i.e., 15/2 hours = 7.5 hours = 7 hours and 30 minutes.

**Question 2**

There is a building with 4 floors and each floor has equal area. There are three sweepers P, Q and R. P can clean 1 floor in 10 hours, Q can clean 8/5 of the floors in 40 hours and R can clean 4/3 of the floors in 13 hours. Then who will clean all the 4 floors at first?

a) R b) R & P c) Q d) Q & P

**Answer :**a) R

Solution :

P can sweep 1 floor in 10 hours.

Then 4 floors will be cleaned by P in = 10 x 4 = 40 hours.

Then 4 floors will be cleaned by P in = 10 x 4 = 40 hours.

Q can sweep 8/5 part in 40 hours.

Then 1 floor will be done by Q in 40/(8/5) = 25 hours.

And 4 floors will be done by Q in 25 x 4 = 100 hours.

Then 1 floor will be done by Q in 40/(8/5) = 25 hours.

And 4 floors will be done by Q in 25 x 4 = 100 hours.

R can clean 4/3 part of the floors in 13 hours.

Then 1 floor will be cleaned by R in 13/(4/3) = 13 x 3/4 hours.

And 4 floors will be done by R in 13 x 3/4 x 4 = 13 x 3 = 39 hours.

Then 1 floor will be cleaned by R in 13/(4/3) = 13 x 3/4 hours.

And 4 floors will be done by R in 13 x 3/4 x 4 = 13 x 3 = 39 hours.

Thus P, Q and R takes 40, 100 and 39 hours respectively.

Hence the sweeper R will complete the work at first.

Hence the sweeper R will complete the work at first.

**Question 3**

A man and his son planned to paint their own house. The man alone can do in 20 days. He paints for 4 days and then his son completed in 8 days. Find how many days will they take working together?

a) 12 days b) 11 days c) 7 days d) 8 days

**Answer :**c) 7 days

Solution :

Man's 1 day work = 1/20

Then 4 days work = 4/20 = 1/5

Remaining work = 1 - 1/5 = 4/5

Then 4 days work = 4/20 = 1/5

Remaining work = 1 - 1/5 = 4/5

Now, 4/5 work is done by the son in 8 days.

Then, whole work will be done by him in (8 x 5/4) days = 10 days.

Then his 1 day work = 1/10

Then, whole work will be done by him in (8 x 5/4) days = 10 days.

Then his 1 day work = 1/10

The man and his son's 1 day work = 1/10 + 1/10 = 3/10

They will complete the work together in 20/3 days = 6 2/3 days = 7 days(nearly).

Hence the answer is 7 days.

They will complete the work together in 20/3 days = 6 2/3 days = 7 days(nearly).

Hence the answer is 7 days.