Quantitative GMAT Time and Work Problems and Solutions: Sample Numericals For Practice

The GMAT examination asks you a few interesting sums based on the work and time topic. You, as a candidate, will have to keep in mind that you need to find the rate of work happening and that’s basically it:

Work Rate = Total Work / Time Taken.

Below, we have provided a few practice problems for your preparations. Let’s go through them all without any further ado.

Question 1

A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is :

A. 1/4

B. 1/10

C. 7/15

D. 8/15

Solution:

A's 1 day's work = 1/15;

B's 1 day's work = 1/20;

(A + B)'s 1 day's work =(1/15 + 1/20) = 7/60.

(A + B)'s 4 day's work = (7/60 x 4) = 7/15.

Therefore, Remaining work = (1 – 7/15) = 8/15.

Answer: Option D

2. A can lay railway track between two given stations in 16 days and B can do the same job in 12 days. With help of C, they did the job in 4 days only. Then, C alone can do the job in:

A. 9 1/5 days

B. 9 2/5 days

C. 9 3/5 days

D. 10 days

Solution:

(A + B + C)'s 1 day's work = 1/4,

A's 1 day's work = 1/16.

B's 1 day's work = 1/12.

Therefore C's 1 day's work = 1/4 - (1/16 + 1/12) = (1/4 – 7/48) = 5/48.

So, C alone can do the work in 48/5 = 9 3/5 days.

Answer: Option C

3. A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?

A. 12 days

B. 15 days

C. 16 days

D. 18 days

Solution:

A's 2 day's work = (1/20 x 2) = 1/10.

(A + B + C)'s 1 day's work = 1/20 + 1/30 + 1/60 = 6/60 = 1/10.

Work done in 3 days = 1/10 + 1/10 = 1/5.

Now, 1/5 work is done in 3 days.

Therefore, the whole work will be done in (3 x 5) = 15 days.

Answer: Option B

4. A is thrice as good as workman as B and therefore is able to finish a job in 60 days less than B. Working together, they can do it in:

A. 20 days

B. 22 ½ days

C. 25 days

D. 30 days

Solution:

Ratio of times taken by A and B = 1 : 3.

The time difference is (3 - 1) 2 days while B take 3 days and A takes 1 day.

If the difference of time is 2 days, B takes 3 days.

If the difference of time is 60 days, B takes (3/2 x 60) = 90 days.

So, A takes 30 days to do the work.

A's 1 day's work = 1/30

B's 1 day's work = 1/90

(A + B)'s 1 day's work = 1/30 + 1/90 = 4/90 = 2/45

A and B together can do the work in 45/2 = 22 ½ days.

Answer: Option B

5. A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?

A. Rs. 375

B. Rs. 400

C. Rs. 600

D. Rs. 800

Solution:

C's 1 day's work = 1/3 – (1/6 + 1/8) = 1/3 – 7/24 = 1/24.

A's wages : B's wages : C's wages = 1/6 : 1/8 : 1/24 = 4 : 3 : 1.

C's share (for 3 days) = Rs. (3 x 1/24 x 3200) = Rs. 400.

Answer: Option B

6. A and B can complete a work in 15 days and 10 days respectively. They started doing the work together, but after 2 days B had to leave and A alone completed the remaining work. The whole work was completed in :

A. 8 days

B. 10 days

C. 12 days

D. 15 days

Solution:

(A + B)'s 1 day's work = (1/15 + 1/10) = 1/6.

Work done by A and B in 2 days = (1/6 x 2)= 1/3.

Remaining work = (1 – 1/3) = 2/3.

Now, 1/15 work is done by A in 1 day.

Therefore, 2/3 work will be done by A in (15 x 2/3) = 10 days.

Hence, total time taken = (10 + 2) = 12 days.

Answer: Option C

 

All the best for GMAT 2018!