7: Ratio and Proportion

Example number 7.1, Page number 7.3

In [1]:
#importing modules
import math
from __future__ import division

#Variable declaration
a=0.75;
b=5;
c=8;

#Calculation
x=a*c/b;

#Result
print "result is",x

result is 1.2

Example number 7.2, Page number 7.3

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

#Variable declaration
a=0.32;
b=0.02;

#Calculation
x2=a*b;
x=math.sqrt(a*b);    #mean proportion

#Result
print "mean proportion is",x

mean proportion is 0.08

Example number 7.3, Page number 7.3

In [4]:
#importing modules
import math
from __future__ import division

#Variable declaration
a=16;
b=24;

#Calculation
x=(b**2)/a;     #third proportional

#Result
print "third proportional is",x

third proportional is 36.0

Example number 7.4, Page number 7.3

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

#Variable declaration
a=16;
b=4;

#Calculation
x=(b**2)/a;     #third proportional

#Result
print "third proportional is",x

third proportional is 1.0

Example number 7.5, Page number 7.3

In [8]:
#importing modules
import math
from __future__ import division
from fractions import Fraction

#Variable declaration
a=3/48;
b=1/12;

#Calculation
p=a/b;      #part

#Result
print "part is",Fraction(p)

part is 3/4

Example number 7.6, Page number 7.3

In [11]:
#importing modules
import math
from __future__ import division
from fractions import Fraction

#Variable declaration
a=7;
b=8;

#Calculation
p=a/b;      #part

#Result
print "part is",Fraction(p)

part is 7/8

Example number 7.7, Page number 7.4

In [12]:
#importing modules
import math
from __future__ import division

#Variable declaration
a=4/3;     #ratio of number of boys and girls
b=480;    #number of boys

#Calculation
x=b/a;    #number of girls

#Result
print "number of girls is",x

number of girls is 360.0

Example number 7.8, Page number 7.4

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

#Variable declaration
a=4;     #first ratio term
b=5;     #second ratio term
c=72;    #total amount(Rs)

#Calculation
fp=a*c/(a+b);   #first part(Rs)
sp=b*c/(a+b);   #second part(Rs)

#Result
print "first part is",fp,"Rs"
print "second part is",sp,"Rs"

first part is 32.0 Rs
second part is 40.0 Rs

Example number 7.9, Page number 7.4

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

#Variable declaration
a=2;     #first ratio term
b=5;     #second ratio term
c=350;   #number of students

#Calculation
x=b*c/(a+b);   #number of girls

#Result
print "number of girls is",x

number of girls is 250.0

Example number 7.10, Page number 7.4

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

#Variable declaration
a=3;   #first ratio term
b=7;   #second ratio term
lcm=210;   #lcm of two numbers

#Calculation
x=lcm/(a*b);   #factor
n1=a*x;   #first number
n2=b*x;   #second number

#Result
print "the numbers are",n1,"and",n2

the numbers are 30.0 and 70.0

Example number 7.11, Page number 7.4

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

#Variable declaration
a=3;   #first ratio term
b=7;   #second ratio term
c=33;   #antecedent

#Calculation
x=b*c/a;   #consequent

#Result
print "consequent is",x

consequent is 77.0

Example number 7.12, Page number 7.4

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

#Variable declaration
aold=3;   #first ratio term
bold=5;   #second ratio term
c=4;   #increment
anew=2;   #first term of new ratio
bnew=3;   #second term of new ratio

#Calculation
Nr=(aold*c)-(anew*c);
Dr=(bold*anew)-(aold*bnew);
x=Nr/Dr;     #factor
n1=x*aold;
n2=x*bold;  

#Result
print "the numbers are",n1,"and",n2

the numbers are 12.0 and 20.0

Example number 7.13, Page number 7.4

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

#Variable declaration
aold=12;   #first ratio term
bold=13;   #second ratio term
c=20;   #decrement
anew=2;   #first term of new ratio
bnew=3;   #second term of new ratio

#Calculation
Nr=(bnew*c)-(anew*c);
Dr=(bnew*aold)-(anew*bold);
x=Nr/Dr;     #factor
n1=x*aold;
n2=x*bold;  

#Result
print "the numbers are",n1,"and",n2

the numbers are 24.0 and 26.0

Example number 7.14, Page number 7.4

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

#Variable declaration
aold=3;   #first ratio term
bold=7;   #second ratio term
anew=2;   #first term of new ratio
bnew=5;   #second term of new ratio

#Calculation
Nr=(aold*bnew)-(anew*bold);
Dr=bnew-anew;
x=Nr/Dr;    #decrement

#Result
print "decrement is",round(x,2)
print "answer given in the book is wrong"

decrement is 0.33
answer given in the book is wrong

Example number 7.15, Page number 7.5

In [21]:
#importing modules
import math
from __future__ import division

#Variable declaration
aold=1;   #first ratio term
bold=2;   #second ratio term
anew=1;   #first term of new ratio
bnew=3;   #second term of new ratio
g=2;   #number of gents left
l=2;   #number of ladies left

#Calculation
Nr=(g*bnew)-(anew*l);
Dr=bnew-(anew*l);
x=Nr/Dr;    #factor
n=x*(aold+bold);     #number of people originally present

#Result
print "number of people originally present is",n

number of people originally present is 12.0

Example number 7.16, Page number 7.5

In [22]:
#importing modules
import math
from __future__ import division

#Variable declaration
c1=1;     #coin value 1 rupee
c2=0.5;   #coin value 50 paise
c3=0.25;  #coin value 25 paise
t=35;     #total amount(Rs)

#Calculation
n=t/(c1+c2+c3);     #number of each type of coin(coins)

#Result
print "number of each type of coin is",n,"coins"

number of each type of coin is 20.0 coins

Example number 7.17, Page number 7.5

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

#Variable declaration
a=3/7;
b=1/5;
c=7/15;

#Calculation
x=a*b/c;      #fraction of same ratio

#Result
print "fraction of same ratio is",x

fraction of same ratio is 0.183673469388

Example number 7.18, Page number 7.5

In [26]:
#importing modules
import math
from __future__ import division

#Variable declaration
s=90;    #sum of ages of A, B, C(years)
n=6;     #number of years ago
a=1;     #ratio term for age of A
b=2;     #ratio term for age of B
c=3;     #ratio term for age of C

#Calculation
age=s-(n*c);    #sum of ages of A, B, C 6 years ago(years)
C=c*age/(a+b+c);    #age of C 6 years ago(years)
Cp=C+a+b+c;         #present age of C(years)

#Result
print "present age of C is",Cp,"years"

present age of C is 42.0 years

Example number 7.19, Page number 7.5

In [27]:
#importing modules
import math
from __future__ import division

#Variable declaration
s=532;     #sum of squares of 3 numbers
a=3;      #first term of ratio
b=2;      #second term of ratio

#Calculation
n1=a*a;   #first number
n2=a*b;   #second number
n3=b*b;   #third number
x2=s/((n1**2)+(n2**2)+(n3**2));
x=math.sqrt(x2);     #factor
N2=n2*x;     #second number

#Result
print "second number is",N2

second number is 12.0

Example number 7.20, Page number 7.6

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

#Variable declaration
l1=60;     #length of wire(m)
w1=80;     #weight of wire(kg)
l2=141;    #length of another wire(m)

#Calculation
x=w1*l2/l1;    #weight of wire(kg)

#Result
print "weight of wire is",x,"kg"

weight of wire is 188.0 kg

Example number 7.21, Page number 7.6

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

#Variable declaration
bc=1;    #first term of ratio
ac=2;    #second term of ratio
ab=3;    #third term of ratio

#Calculation
#abyb=ac/bc
a=ac;
b=bc;
result=(a**2)/(b**2);     #value of a/bc : b/ca

#Result
print "value of a/bc : b/ca is",int(result)

value of a/bc : b/ca is 4

Example number 7.23, Page number 7.6

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

#Variable declaration
v1=1;     #one rupee coin
v2=1/2;   #50 paise coin
v3=1/4;   #25 paise coin
v4=1/10;   #10 paise coin
n1=1;   #number of 1 rupee coins
n2=3;   #number of 50 paise coins
n3=5;   #number of 25 paise coins
n4=7;   #number of 10 paise coins
s=22.25;    #total amount(Rs)

#Calculation
a=(v1*n1)+(v2*n2)+(v3*n3)+(v4*n4);
x=s/a;     #factor
N1=x*n1;   #number of 1 rupee coins
N2=x*n2;   #number of 50 paise coins
N3=x*n3;   #number of 25 paise coins
N4=x*n4;   #number of 10 paise coins

#Result
print "number of 1 rupee coins is",N1
print "number of 50 paise coins is",N2
print "number of 25 paise coins is",N3
print "number of 10 paise coins is",N4

number of 1 rupee coins is 5.0
number of 50 paise coins is 15.0
number of 25 paise coins is 25.0
number of 10 paise coins is 35.0

Example number 7.24, Page number 7.7

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

#Variable declaration
a=1/3;
b=1/4;
c=1/5;
d=1/6;

#Calculation
l1=(1/a)*(1/b)/gcd(1/a,1/b);
l2=(1/c)*(1/d)/gcd(1/c,1/d);
l=l1*l2/gcd(l1,l2);           #lcm of 3,4,5,6
A=a*l;
B=b*l;
C=c*l;
D=d*l;
p=A+B+C+D;

#Result
print "the person should have atleast",p,"pens"

the person should have atleast 57.0 pens