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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.
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 and A+C can do a work in 10 days.
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:
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