Aptitude - Part 1

A can do a unit of work in n days then working uniformly
A's one day work = 1/n -----------------(1)

Almost all work problems will make use of the formula below
if for a unit of work
A ---------  t1 days
B ---------- t2 days
we find one days work in such case here it is
A's --------one day work ---------- 1/t1
B's -------- one day work ---------- 1/t2
we add the work of persons not their time
A+B ----------one day work ---------- 1/t1+1/t2   --------------(2)

A+B ----------1/days work ------------ t1t2/t1+t2 days       ---------------------(3)
For a unit of work if
n person                -------        tdays
m person(m<n)  -------         t (n/m) days
                (m>n)    -------          t(m/n) day
Example It takes 4 men to finish work in 10 day. How many days will be required if only i)2 men work or ii)10 men work
For less men we would need more days
2 men would need 10(4/2) = 20 days
10 men would need 10(4/10) = 4 days

If na1 persons in group A can do  a piece of work in ta1 days. It takes na2(na2 > na1) persons from group B to do same piece of work in tb2 days. If na2 persosns from group A and nb2 persons from s group B works together how much time will it take


For a unit of work
na1 --------------- ta1 days
na2(na2 > na1) --------------- ta1(na1/na2) days

nb1--------------tb1 days
nb2(nb2<na1) <="" p="">

If 4 men or 6 women or 10 girls can do a piece of work in 10 days How many days are required for 3 men 8 women and 6 girls
Solution
For a unit of work
4men --------------10days
3men--------------10(4/3)days

6 women ----------------10days
8 women----------------10(6/8)days

10girls-----------------10days
6girls-------------------10(10/6)days

3men+8wome+6girl -------one days work ------- 3/40 + 8/60 + 6/100
for a unit of work
3men+8wome+6girl ------------------ ------- 1/(3/40 + 8/60 + 6/100)

If B is p% more efficient than A then
for unit of work
B--------------xdays
A-------------x(1+pf)days

If B is 100% more efficient than B then
A------------x(1+1) =2x  A takes twice the time B takes

If B is 40% more efficient than B then
A ------------x(1+.4)=1.4x

Poblem A is thrice as good a workman as B and therefore is able to finish a job in 60 days less than B. Working together, they can do it in:
Solution
let time taken by A to finish work be x
time taken by B would be 3x
and difference of their time is given as 3x - x = 60
x=30
so B time is 90
one days work of A+B = 1/30+1/90