How to solve Time & Work (Shortcut Approach) - Part I

Time and Work is an important topic asked under the Arithmetic section in Quantitative Aptitude. Today we are sharing with you some important questions asked under Time and work topic along with various approaches that you can follow to solve these questions. We will continue this topic in various parts. In this part, we will discuss the basic questions that are usually asked in this topic and how you can solve them using the normal as well as Shortcut approach. There will be four parts of this topic and as we moved forward, the level of questions will also increase. This basic shortcut is necessary to understand upcoming articles.

After going through these questions, make sure that you attempt the quiz at the end of the article to make sure that you understand these questions clearly. In case of any query, leave a comment and we will try to solve it for you.

Example 1                                                        

A takes 8 days to finish a piece of work. B takes 10 days to finish the same work. How long will it take to finish the work when both of them are working together?

Solution

Basic Approach:

Now for such questions, A’s 1-day work = 1/8
B’s 1-day work = 1/10
Work done by both A and B together in one day = 1/8 + 1/10 = 9/40

Hence, A and B together will finish the work in 40/9 days.

While taking exam, you can express the information provided in the undermentioned form so that it consumes less time and space.

Example 2

A takes 8 day to finish a piece of work. B takes 10 days to finish the same work. C takes 20 days to finish the work. How long will it take to finish the work when all are working together ?

Solution

Example 3

A takes 8 day to finish a piece of work. B takes 10 days to finish the same work. C takes 20 days to finish the work. D takes 40 days to finish the work. How long will it take to finish the work when all of them are working together ?

Solution

Example 4

B and C together can complete the work in 8 days. A and B together can complete the same work in 12 days while A and C together can complete it in 16 days 
find 
(a) In how many days A, B and C together can complete the same work ?
(b) In how many days A alone can complete the work ?
(c) In how many days B alone can complete the work ?
(d) In how many days C alone can complete the work ?
 

Solution

(a) In how many days A, B and C together can complete the same work?

(b) In how many days A alone can complete the work ?

(c) In how many days B alone can complete the work?

(d) In how many days C alone can complete the work?

Example 5

If A+B can do a work in 10 days and A alone can complete the same work in 15 days. Find the no. of days taken by B to complete the work alone ?

Solution

Example 6

If (A+B+C) can do a work in 6 days, A+B can do a work in 8 days and A+C can do a work in 10 days.find the time taken by A,B and c individually and (B+C) together ?

Solution

Example 7

Rohit can do a piece of work in 10 days, but with the help of Amit, he can do the same work in 6 days. In what time Amit can do the same work alone ?

Solution

Example 8:

There are two gardeners A and B. Both plant some no. of trees in a garden in 10 days and 16 days respectively. In how many days both can complete the work together?

Solution:

Now let’s discuss this same question by a different approach.

 When time taken by A and B respectively is given, we can find the ratio of efficiency of A and B by taking inverse of their time.

Let’s do some examples to calculate efficiency.

Example 9:

If A and B alone do the same work in 14 and 18 days respectively, then ratio of efficiency of A and B.

Solution:

Example 10 :

If A and B together complete the work in 10 days and B alone complete the same work in 15 days. In how many days can A alone complete the same work ?

Solution:

Example: 11

A is thrice as good as workman as B. Together they can finish a work in 12 days. In how many days will A finish the same work alone ?

Solution: