9: Mixtures

Example number 9.1, Page number 9.4

In [2]:
#importing modules
import math
from __future__ import division

#Variable declaration
c1=9.5;      #cost of oil per kg(Rs)
c2=10;       #cost of another oil(Rs)
Cm=9.6;      #cost of mixture(Rs)

#Calculation
q1byq2=(c2-Cm)/(Cm-c1);     #proportion to be mixed

#Result
print "proportion to be mixed is",int(q1byq2)

proportion to be mixed is 4

Example number 9.2, Page number 9.4

In [5]:
#importing modules
import math
from __future__ import division

#Variable declaration
c1=25;      #percentage of alcohol(%)
c2=50;       #percentage of alcohol(%)
Cm=40;      #alcohol strength(%)

#Calculation
q1byq2=(c2-Cm)/(Cm-c1);     #proportion to be mixed

#Result
print "proportion to be mixed is",q1byq2

proportion to be mixed is 0.666666666667

Example number 9.3, Page number 9.5

In [6]:
#importing modules
import math
from __future__ import division

#Variable declaration
c1=8;      #first part(%)
c2=10;       #second part(%)
Cm=9.2;      #yearly average(%)
A=1000;      #amount(Rs)

#Calculation
q1=c2-Cm;
q2=Cm-c1;     
A1=q1*A/(q1+q2);      #quantity of money lent at 8%(Rs)
A2=q2*A/(q1+q2);      #quantity of money lent at 10%(Rs)

#Result
print "quantity of money lent at 8% is",A1,"Rs"
print "quantity of money lent at 10% is",A2,"Rs"

quantity of money lent at 8% is 400.0 Rs
quantity of money lent at 10% is 600.0 Rs

Example number 9.4, Page number 9.5

In [13]:
#importing modules
import math
from __future__ import division

#Variable declaration
c1=0;      #pure milk(litres)
c2=3.6;       #cost of pure milk(Rs)
Cm=3;      #cost of mixture(Rs)

#Calculation
q1byq2=(Cm-c1)/(c2-Cm);     #amount of water to be added(litres)

#Result
print "amount of water to be added is",q1byq2,"litres"

amount of water to be added is 5.0 litres

Example number 9.5, Page number 9.5

In [14]:
#importing modules
import math
from __future__ import division

#Variable declaration
c1=24;      #cost of salt(paise)
c2=42;      #cost of salt(paise)
c=40;       #cost of mixture(paise)
e=25;       #efficiency(%) 

#Calculation
Cm=c*100/(100+e);      #cost price of mixture(paise)
q1byq2=(Cm-c1)/(c2-Cm);      #proportion to be mixed
q=q1byq2*e;        #amount of salt(kg)

#Result
print "amount of salt is",q,"kg"

amount of salt is 20.0 kg

Example number 9.6, Page number 9.5

In [15]:
#importing modules
import math
from __future__ import division

#Variable declaration
a=5;       #amount of alcohol solution(litres)
p=20/100;    #percentage of solution

#Calculation
A=p*a;      #amount of alcohol(litre)
S=A*100/(A+a);    #strength of alcohol(%)

#Result
print "strength of alcohol is",S,"%"

strength of alcohol is 16.6666666667 %

Example number 9.7, Page number 9.6

In [16]:
#importing modules
import math
from __future__ import division

#Variable declaration
p1=90/100;      #percentage of milk in mixture(%)
p2=10/100;      #percentage of water in mixture(%)
a=40;       #amount of mixture(litres)
p_2=20;     #new percent of water(%)

#Calculation
A=(p1*a*p_2/(100-p_2))-(p2*a);     #amount of water to be added(litres)

#Result
print "amount of water to be added is",A,"litres"

amount of water to be added is 5.0 litres

Example number 9.8, Page number 9.6

In [17]:
#importing modules
import math
from __future__ import division

#Variable declaration
c1=0;      
c2=3.0;      #cost of pure milk(Rs)
e=20/100;       #efficiency(%) 

#Calculation
Cm=c2/(1+e);    #CP of mixture(Rs)
q1byq2=(Cm-c1)/(c2-Cm);      #proportion to be mixed
A=q1byq2**2;        #amount of pure milk(litres)

#Result
print "amount of pure milk is",A,"litres"

amount of pure milk is 25.0 litres

Example number 9.9, Page number 9.6

In [18]:
#importing modules
import math
from __future__ import division

#Variable declaration
a1=6;     #amount of tea(kg)
p1=6;     #cost of tea(Rs)
a2=4;     #amount of tea(kg)
p2=7;     #cost of tea(Rs)
p=10/100;    #profit(p)

#Calculation
cp=((a1*p1)+(a2*p2))/(a1+a2);       #cost price of mixture(Rs)
sp=(1+p)*cp;           #selling price of mixture(Rs)

#Result
print "selling price of mixture is Rs",sp,"per kg"

selling price of mixture is Rs 7.04 per kg

Example number 9.10, Page number 9.6

In [19]:
#importing modules
import math
from __future__ import division

#Variable declaration
p1=20;    #percentage of sulphuric acid(%)
q1=5;     #amount of acid(litres)
p2=100;   #percentage of pure sulphuric acid(%)
q2=5;     #amount of acid(litres)

#Calculation
s=((p1*q1)+(p2*q2))/(q1+q2);    #strength of acid in mixture(%)

#Result
print "strength of acid in mixture is",s,"%"

strength of acid in mixture is 60.0 %

Example number 9.11, Page number 9.6

In [20]:
#importing modules
import math
from __future__ import division

#Variable declaration
q1=3
q2=2;        
c=11;     #cost at which mixture is sold(Rs)
p=10/100;     #profit(%)

#Calculation
Cm=c/(1+p);    #cost price of mixture(Rs)
x=((q2*Cm)+(q1*Cm)+(q2*q2))/(q1+q2);      #cost price of 1st liquid(Rs)
x2=x-q2;      #cost price of 2nd liquid(Rs)

#Result
print "cost price of 1st liquid is Rs",x,"per litre"
print "cost price of 2nd liquid is Rs",x2,"per litre"

cost price of 1st liquid is Rs 10.8 per litre
cost price of 2nd liquid is Rs 8.8 per litre

Example number 9.12, Page number 9.7

In [23]:
#importing modules
import math
from __future__ import division

#Variable declaration
a=2;
b=1;       #proportion of 1st mixture of alcohol and water
x=1;
y=1;       #proportion of 2nd mixture of alcohol and water

#Calculation
q1=(a/(a+b))+(x/(x+y));      #quantity of alcohol in 3rd glass
q2=(b/(a+b))+(y/(x+y));      #quantity of water in 3rd glass

#Result
print "alcohol and water are in the proportion of",q1/q2 

alcohol and water are in the proportion of 1.4

Example number 9.13, Page number 9.7

In [24]:
#importing modules
import math
from __future__ import division

#Variable declaration
c1=2.10;      #cost price of coffee(Rs)
q1=15;     #quantity of coffee(parts)
c2=0.98;   #cost price of chicory(Rs)
q2=1;      #quantity of chicory(part)
s=2.25;    #selling price per kg(Rs)
a=500;     #amount(kg)

#Calculation
Cm=((c1*q1)+(c2*q2))/(q1+q2);     #cost price of mixture(Rs)
p=(s-Cm)*a;             #gain made on sale of 5 quintals(Rs)

#Result
print "gain made on sale of 5 quintals is Rs",p

gain made on sale of 5 quintals is Rs 110.0

Example number 9.14, Page number 9.8

In [25]:
#importing modules
import math
from __future__ import division

#Variable declaration
qa=35;       #percentage of alcohol by weight
qw=25;     #weight of water(gms)
m=100;     #total mixture(g)

#Calculation
p=qa*100/(m+qw);      #percentage of alcohol(%)

#Result
print "percentage of alcohol is",p,"%"

percentage of alcohol is 28.0 %

Example number 9.15, Page number 9.8

In [28]:
#importing modules
import math
from __future__ import division

#Variable declaration
Cm=24;     #strength of butt(%)
c1=18;     #percentage of spirit(%)
c2=32;     #percentage of spirit(%)

#Calculation
q1=Cm-c1;    #quantity of 32% spirit
q2=c2-Cm;    #quantity of 18% spirit
f=q2/(q1+q2);     #quantity of the butt stolen

#Result
print "quantity of the butt stolen is",round(f,2)

quantity of the butt stolen is 0.57

Example number 9.16, Page number 9.8

In [29]:
#importing modules
import math
from __future__ import division

#Variable declaration
m=66;    #mixture of milk(litres)
a=5;
b=1;     #ratio of milk and water
x=5;
y=3;     #new ratio  

#Calculation
x1=a*m*y/(a+b);
x2=a*m/(x+b);
x=(x1-x2)/a;     #quantity of water added(litres)

#Result
print "quantity of water added is",x,"litres"

quantity of water added is 22.0 litres

Example number 9.17, Page number 9.8

In [30]:
#importing modules
import math
from __future__ import division

#Variable declaration
qw1=72/100;       #content of water in fresh fruit(%)
a=100;     #amount of fresh fruit(kg)
qw2=20/100;       #content of water in dry fruit(%)

#Calculation
x=(1-qw1)*a/(1-qw2);       #amount of dry fruit obtained(kg)

#Result
print "amount of dry fruit obtained is",x,"kg"

amount of dry fruit obtained is 35.0 kg

Example number 9.18, Page number 9.8

In [31]:
#importing modules
import math
from __future__ import division

#Variable declaration
qs=5/100;     #content of salt by water(%)
a=60;         #amount of sea water(kg)
q=3;      #content of salt in solution(%)

#Calculation
x=((qs*a*100)-(q*a))/q;         #quantity of fresh water to be added(kg)

#Result
print "quantity of fresh water to be added is",x,"kg"

quantity of fresh water to be added is 40.0 kg

Example number 9.19, Page number 9.9

In [32]:
#importing modules
import math
from __future__ import division

#Variable declaration
qa=1;     #copper in 1st alloy
qb=1;     #copper in 2nd alloy
x=3;
y=4;      #ratio of copper to zinc
a=5;
b=2;      #ration of copper to zinc in new alloy
q=28;     #quantity of new alloy(kg) 

#Calculation
Cm=qa/(qa+qb);      #copper in new alloy
c1=x/(x+y);         #copper in 2nd alloy
c2=a/(a+b);         #copper in 1st alloy
q1=(Cm-c1);
q2=(c2-Cm);
a1=q1*q/(q1+q2);    #amount of 1st alloy(kg)
a2=q-a1;            #amount of second alloy(kg)

#Result
print "amount of first alloy is",a1,"kg"
print "amount of second alloy is",a2,"kg"

amount of first alloy is 7.0 kg
amount of second alloy is 21.0 kg

Example number 9.20, Page number 9.9

In [33]:
#importing modules
import math
from __future__ import division

#Variable declaration
a1=4;
b1=1;       #relation of copper and zinc
a2=1;
b2=3;       #relation of copper and zinc
a3=3;
b3=2;       #ratio of copper to zinc 
q1=10;      #amount of 1st alloy(kg)
q2=16;      #amount of 2nd alloy(kg)

#Calculation
c1=a1*q1/(a1+b1);      #copper in 1st alloy
c2=a2*q2/(a2+b2);      #copper in 2nd alloy
x=(a3*(q1+q2))-((a3+b3)*(c1+c2));       
w=(x/2)+q1+q2;      #weight of new alloy(kg)

#Result
print "weight of new alloy is",w,"kg"

weight of new alloy is 35.0 kg

Example number 9.21, Page number 9.10

In [34]:
#importing modules
import math
from __future__ import division

#Variable declaration
a=39;     #amount(Rs)
s=45;     #number of boys and girls
c1=50/100;    #amount girl gets(Rs)
c2=1;         #amount boy gets(Rs)

#Calculation
Cm=a/s;
qb=(Cm-c1);     #number of boys in ratio
qg=(c2-Cm);     #number of girls in ratio
b=qb*s/(qb+qg);     #number of boys
g=s-b;              #number of girls

#Result
print "number of boys is",b
print "number of girls is",g

number of boys is 33.0
number of girls is 12.0

Example number 9.22, Page number 9.10

In [35]:
#importing modules
import math
from __future__ import division

#Variable declaration
co=9/100;      #content of oxygen
vo=16/100;     #volume of oxygen
q=8;       #quantity of cylinder(litre)

#Calculation
r=math.sqrt(co*q/(vo*q));
R=q*(1-r);     #quantity of mixture released(litres)

#Result
print "quantity of mixture released is",R,"litres"

quantity of mixture released is 2.0 litres

Example number 9.23, Page number 9.10

In [36]:
#importing modules
import math
from __future__ import division

#Variable declaration
x0=100;     #original amount of milk(kg)
xr=10;      #amount of milk removed(kg)
n=3;        #number of operations

#Calculation
a=x0*(1-(xr/x0))**n;       #amount of milk left(kg)

#Result
print "amount of milk left is",a,"kg"

amount of milk left is 72.9 kg

Example number 9.24, Page number 9.11

In [44]:
#importing modules
import math
from __future__ import division

#Variable declaration
x0=1;     #quantity of dettol(litre)
xr=1/3;      #quantity of dettol removed(litre)
n=4;        #number of operations

#Calculation
Aa=(1-(xr/x0))**n;       #amount of dettol left(litre)
Ba=1-Aa;                 #amount of water left(litre)
r=Aa/Ba;                 #ratio of dettol and water 

#Result
print "ratio of dettol and water is",round(r,2)

ratio of dettol and water is 0.25

Example number 9.25, Page number 9.12

In [40]:
#importing modules
import math
from __future__ import division

#Variable declaration
a1=5;      #parts of after shave lotion
b1=3;      #parts of water
Al=1/2;               #amount of after shave lotion

#Calculation
Ap=a1/(a1+b1);      #amount of after shave lotion present
R=1-(Al/Ap);        #part of the mixture taken out

#Result
print "part of the mixture taken out is",R

part of the mixture taken out is 0.2

Example number 9.26, Page number 9.12

In [41]:
#importing modules
import math
from __future__ import division

#Variable declaration
c1=12;       #cost price of 1st variety(Rs)
c2=14.40;    #cost price of 2nd variety(Rs)
c3=17.40;    #cost price of 3rd variety(Rs)
Cm=14.10;    #cost price of mixture(Rs)
f=11.11;     #factor to be rounded off

#Calculation
q1=(c2-Cm)*(c3-Cm)*f;     #quantity of 1st variety(kg)
q2=(Cm-c1)*(c3-Cm)*f;     #quantity of 2nd variety(kg)
q3=(c2-Cm)*(Cm-c1)*f;     #quantity of 3rd variety(kg)


#Result
print "three kinds of rice are mixed in the ratio",round(q1),":",round(q2),":",round(q3)

three kinds of rice are mixed in the ratio 11.0 : 77.0 : 7.0