Time & Work
Rules:
If P can do a piece of work in ‘n’ days, then P’s one day’s work is 1/n.
If P’s 1 day’s work = 1/n, then P can finish the work in ‘n’ days.
If P is twice as good a workman as Q, then:
Ratio of work done by P and Q = 2:1
Ratio of times taken by P & Q to finish a work = 1:2
Ex1: P can do a work in 8 days which Q alone can do in 10 days. How many days will it take to finish if both working together?
Sol: P’s 1 day’s work = 1/8
èQ’s 1 day’s work = 1/10
è(P+Q)’s 1 day’s work = [1/8 + 1/10] è 18/80
:: Both will finish the work in 80/18 è 4[8/18]
Ex2: Jhon and David working together can do a work in 6hours while Jhone alone can do the same work in 10hours. In how many hours David alone can do that work.
Sol: (Jhon+David)’s 1hour work = 1/6
èJhon’s 1hour’s work = 1/10
èDavid’s 1hour’s work = [1/6+1/10]
ð 16/60
ð Hence David alone can do that work in 60/16 => 3.75hours
Ex3: Anil(A) and Sunil(S) can do a work in 10days. Sunil and Mahesh can do it in 12days. Anil and Mahesh(M) can do it in 14days. In how many days will Anil, Sunil and Mahesh finish if all working together?
Sol: (A+S)’s 1day’s work = 1/10
è(S+M)’s 1day’s work = 1/12
è(A+M)’s 1day’s work = 1/14
After adding all è (A+S)+(S+M)+(A+M) = [1/10+1/12+1/14]
è2(A+S+M) = 428/1680 This is A+S+M 1day’s work
è A,S and M can finish this work together in (1680*2)/428 = 7.85days
You could also look at below shortcut technics:
How To Solve Simplification Arithmetic Aptitude Questions
How To Solve Average Arithmetic Aptitude Questions
You could also look at below shortcut technics:
How To Solve Simplification Arithmetic Aptitude Questions
How To Solve Average Arithmetic Aptitude Questions