In [1]:

```
#importing modules
import math
from __future__ import division
#Variable declaration
t1=20; #number of days A can do a job
t2=30; #number of days B can do a job
#Calculation
T=t1*t2/(t1+t2); #number of days for A and B to do the job together
#Result
print "A and B can do the job together in",T,"days"
```

In [2]:

```
#importing modules
import math
from __future__ import division
#Variable declaration
t1=28; #number of days B can do a job
T=12; #number of days for A and B to do the job together
#Calculation
t2=T*t1/(t1-T); #number of days A can do a job
#Result
print "A can do the job in",t2,"days"
```

In [3]:

```
#importing modules
import math
from __future__ import division
from fractions import gcd
#Variable declaration
T1=12; #work done by A and B together(days)
T2=15; #work done by C and B together(days)
T3=20; #work done by A and C together(days)
#Calculation
l1=T1*T2/gcd(T1,T2); #lcm of T1 and T2
L=l1*T3/gcd(l1,T3); #lcm of the given 3 numbers
a=L/T1;
b=L/T2;
c=L/T3;
T=2*L/(a+b+c); #work done by A, B and C together(days)
Ta=2*L/(a-b+c); #work done by A alone(days)
Tb=2*L/(a+b-c); #work done by B alone(days)
Tc=2*L/(-a+b+c); #work done by C alone(days)
#Result
print "work done by A, B and C together is",T,"days"
print "work done by A alone is",Ta,"days"
print "work done by B alone is",Tb,"days"
print "work done by C alone is",Tc,"days"
```

In [4]:

```
#importing modules
import math
from __future__ import division
#Variable declaration
Ta=10; #alone time of A(days)
TB=3; #number of days B worked(days)
Tb=15; #alone time of B(days)
#Calculation
T=Ta*(1-(TB/Tb)); #total work finished(days)
#Result
print "total work is finished in",T,"days"
```

In [5]:

```
#importing modules
import math
from __future__ import division
from fractions import gcd
#Variable declaration
Ta=20; #alone time of A(days)
Tb=30; #alone time of B(days)
a=5; #number of days A leaves(days)
#Calculation
L=Ta*Tb/gcd(Ta,Tb); #lcm of T1 and T2
l1=L/Ta;
l2=L/Tb;
T=(L+(l1*a))/(l1+l2); #total work finished(days)
#Result
print "total work is finished in",T,"days"
```

In [7]:

```
#importing modules
import math
from __future__ import division
from fractions import gcd
#Variable declaration
Ta=10; #alone time of A(days)
Tb=12; #alone time of B(days)
a=6; #number of days after A started(days)
#Calculation
L=T1*T2/gcd(T1,T2); #lcm of T1 and T2
l1=L/Ta;
l2=L/Tb;
T=(L+(l1*a))/(l1+l2); #total work finished(days)
TB=T-a; #number of days B worked for(days)
#Result
print "total work is finished in",T,"days"
print "B worked for",TB,"days"
```

In [8]:

```
#importing modules
import math
from __future__ import division
#Variable declaration
M1=1; #number of men
E1=1; #efficiency of anil
D1=8; #number of days worked(days)
E=60/100; #efficiency of rakesh(%)
P1=1/3; #part of work done by anil
M2=1; #number of men
#Calculation
E2=(M1*M2)+(E1*E); #efficiency
P2=1-P1; #part of work done by rakesh
D2=M1*E1*D1*P2/(P1*E2); #number of days to complete the job(days)
#Result
print "number of days to complete the job is",D2,"days"
```

In [10]:

```
#importing modules
import math
from __future__ import division
from fractions import Fraction
#Variable declaration
T1=5; #work done by A and B together(days)
T=1; #total job done
eB=1/3; #efficiency of B
#Calculation
t=T-(T/T1);
tA=T1*(1/t); #time taken for A to complete the job(days)
x=tA-int(tA);
#Result
print "time taken for A to complete the job is",int(tA),Fraction(x),"days"
```

In [11]:

```
#importing modules
import math
from __future__ import division
#Variable declaration
M1=1; #number of men
D1=12; #number of days worked(days)
M2=1; #number of men
W1=3/4; #work done by A
W2=1/8; #part of work done
#Calculation
d=M1*D1*W2/(W1*M2); #number of days for A(days)
#Result
print "A can finish in",d,"days"
```

In [12]:

```
#importing modules
import math
from __future__ import division
from fractions import gcd
#Variable declaration
Ta=10; #alone time of A(days)
Tb=12; #alone time of B(days)
Tc=15; #alone time of C(days)
a=2; #number of days after A started(days)
b=3; #number of days before the work finished(days)
#Calculation
L1=Ta*Tb/gcd(Ta,Tb); #lcm of Ta and Tb
L=L1*Tc/gcd(L1,Tc); #lcm of all the three
l1=L/Ta;
l2=L/Tb;
l3=L/Tc;
r=1-a/Ta;
T=((r*L)+Tc)/(l2+l3); #total work finished(days)
TB=T-a; #number of days B worked for(days)
#Result
print "total work is finished in",T,"days"
```

In [13]:

```
#importing modules
import math
from __future__ import division
from fractions import gcd
#Variable declaration
T1=15; #alone time of A(days)
T2=10; #alone time of B(days)
a=5; #number of days for B to finish(days)
#Calculation
L=T1*T2/gcd(T1,T2); #lcm of T1 and T2
l1=L/T1;
l2=L/T2;
x=(L-(l2*a))/(l1+l2); #A left after days(days)
#Result
print "A left after",x,"days"
```

In [14]:

```
#importing modules
import math
from __future__ import division
#Variable declaration
T1=12; #alone time of A(days)
T2=15; #alone time of B(days)
T=2; #number of days they work together(days)
t=5; #number of days work is completed(days)
#Calculation
Ta=(1+T+t)*(1/T1); #A's amount of work
Tb=T*(1/T2); #B's amount of work
T3=1-(Ta+Tb);
t3=t/T3; #C can do it in(days)
#Result
print "C can do it alone in",t3,"days"
```

In [18]:

```
#importing modules
import math
from __future__ import division
from fractions import gcd
#Variable declaration
p=25; #amount paid(Rs)
A=32; #number of days for A(days)
B=20; #number of days for B(days)
C=12; #number of days for C(days)
D=24; #number of days for B(days)
#Calculation
l1=A*B/gcd(A,B); #lcm of A and B
l2=C*D/gcd(C,D); #lcm of C and D
L=l1*l2/gcd(l1,l2); #LCM of A,B,C and D
a=L/A;
b=L/B;
c1=(1/C)-(1/B);
c=L*c1;
d=L/D;
Cs=c*p/(a+b+c+d); #amount received by C(Rs)
#Result
print "amount received by C is",round(Cs,2),"Rs"
```

In [24]:

```
#importing modules
import math
from __future__ import division
#Variable declaration
tA=5; #work for A alone(days)
tB=7; #work for B alone(days)
#Calculation
p=round(tA*tB/(tA+tB)); #nearest integer value
Ta=((tA*tB)+(p*(tA-tB)))/tA; #time taken to finish the job if A starts the work(days)
Tb=((tA*tB)-(p*(tA-tB)))/tB; #time taken to finish the job if B starts the work(days)
#Result
print "time taken to finish the job if A starts the work is",Ta,"days"
print "time taken to finish the job if B starts the work is",round(Tb,2),"days"
```

In [26]:

```
#importing modules
import math
from __future__ import division
#Variable declaration
tA=20; #number of days for A(days)
tB=30; #number of days for B(days)
tC=60; #number of days for C(days)
da=3; #help done by A
db=1;
dc=1;
#Calculation
t=(da/tA)+(db/tB)+(dc/tC);
T=da/t; #job is finished in(days)
#Result
print "job is finished in",T,"days"
```

In [27]:

```
#importing modules
import math
from __future__ import division
#Variable declaration
K=3;
l=80; #number of days
#Calculation
T=K*l/((K**2)-1); #job is finished in(days)
#Result
print "job is finished in",T,"days"
```

In [28]:

```
#importing modules
import math
from __future__ import division
#Variable declaration
tA=20; #work by skilled men(days)
tB=30; #work by boys(days)
#Calculation
T=tA*tB/(tA+tB); #time taken if they work together(days)
#Result
print "time taken if they work together is",T,"days"
```