{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#7: Ratio and Proportion"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 7.1, Page number 7.3"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result is 1.2\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=0.75;\n",
"b=5;\n",
"c=8;\n",
"\n",
"#Calculation\n",
"x=a*c/b;\n",
"\n",
"#Result\n",
"print \"result is\",x"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 7.2, Page number 7.3"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"mean proportion is 0.08\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=0.32;\n",
"b=0.02;\n",
"\n",
"#Calculation\n",
"x2=a*b;\n",
"x=math.sqrt(a*b); #mean proportion\n",
"\n",
"#Result\n",
"print \"mean proportion is\",x"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 7.3, Page number 7.3"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"third proportional is 36.0\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=16;\n",
"b=24;\n",
"\n",
"#Calculation\n",
"x=(b**2)/a; #third proportional\n",
"\n",
"#Result\n",
"print \"third proportional is\",x"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 7.4, Page number 7.3"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"third proportional is 1.0\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=16;\n",
"b=4;\n",
"\n",
"#Calculation\n",
"x=(b**2)/a; #third proportional\n",
"\n",
"#Result\n",
"print \"third proportional is\",x"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 7.5, Page number 7.3"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"part is 3/4\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"from fractions import Fraction\n",
"\n",
"#Variable declaration\n",
"a=3/48;\n",
"b=1/12;\n",
"\n",
"#Calculation\n",
"p=a/b; #part\n",
"\n",
"#Result\n",
"print \"part is\",Fraction(p)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 7.6, Page number 7.3"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"part is 7/8\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"from fractions import Fraction\n",
"\n",
"#Variable declaration\n",
"a=7;\n",
"b=8;\n",
"\n",
"#Calculation\n",
"p=a/b; #part\n",
"\n",
"#Result\n",
"print \"part is\",Fraction(p)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 7.7, Page number 7.4"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"number of girls is 360.0\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=4/3; #ratio of number of boys and girls\n",
"b=480; #number of boys\n",
"\n",
"#Calculation\n",
"x=b/a; #number of girls\n",
"\n",
"#Result\n",
"print \"number of girls is\",x"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 7.8, Page number 7.4"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"first part is 32.0 Rs\n",
"second part is 40.0 Rs\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=4; #first ratio term\n",
"b=5; #second ratio term\n",
"c=72; #total amount(Rs)\n",
"\n",
"#Calculation\n",
"fp=a*c/(a+b); #first part(Rs)\n",
"sp=b*c/(a+b); #second part(Rs)\n",
"\n",
"#Result\n",
"print \"first part is\",fp,\"Rs\"\n",
"print \"second part is\",sp,\"Rs\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 7.9, Page number 7.4"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"number of girls is 250.0\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=2; #first ratio term\n",
"b=5; #second ratio term\n",
"c=350; #number of students\n",
"\n",
"#Calculation\n",
"x=b*c/(a+b); #number of girls\n",
"\n",
"#Result\n",
"print \"number of girls is\",x"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 7.10, Page number 7.4"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"the numbers are 30.0 and 70.0\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=3; #first ratio term\n",
"b=7; #second ratio term\n",
"lcm=210; #lcm of two numbers\n",
"\n",
"#Calculation\n",
"x=lcm/(a*b); #factor\n",
"n1=a*x; #first number\n",
"n2=b*x; #second number\n",
"\n",
"#Result\n",
"print \"the numbers are\",n1,\"and\",n2"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 7.11, Page number 7.4"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"consequent is 77.0\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=3; #first ratio term\n",
"b=7; #second ratio term\n",
"c=33; #antecedent\n",
"\n",
"#Calculation\n",
"x=b*c/a; #consequent\n",
"\n",
"#Result\n",
"print \"consequent is\",x"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 7.12, Page number 7.4"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"the numbers are 12.0 and 20.0\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"aold=3; #first ratio term\n",
"bold=5; #second ratio term\n",
"c=4; #increment\n",
"anew=2; #first term of new ratio\n",
"bnew=3; #second term of new ratio\n",
"\n",
"#Calculation\n",
"Nr=(aold*c)-(anew*c);\n",
"Dr=(bold*anew)-(aold*bnew);\n",
"x=Nr/Dr; #factor\n",
"n1=x*aold;\n",
"n2=x*bold; \n",
"\n",
"#Result\n",
"print \"the numbers are\",n1,\"and\",n2"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 7.13, Page number 7.4"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"the numbers are 24.0 and 26.0\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"aold=12; #first ratio term\n",
"bold=13; #second ratio term\n",
"c=20; #decrement\n",
"anew=2; #first term of new ratio\n",
"bnew=3; #second term of new ratio\n",
"\n",
"#Calculation\n",
"Nr=(bnew*c)-(anew*c);\n",
"Dr=(bnew*aold)-(anew*bold);\n",
"x=Nr/Dr; #factor\n",
"n1=x*aold;\n",
"n2=x*bold; \n",
"\n",
"#Result\n",
"print \"the numbers are\",n1,\"and\",n2"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 7.14, Page number 7.4"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"decrement is 0.33\n",
"answer given in the book is wrong\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"aold=3; #first ratio term\n",
"bold=7; #second ratio term\n",
"anew=2; #first term of new ratio\n",
"bnew=5; #second term of new ratio\n",
"\n",
"#Calculation\n",
"Nr=(aold*bnew)-(anew*bold);\n",
"Dr=bnew-anew;\n",
"x=Nr/Dr; #decrement\n",
"\n",
"#Result\n",
"print \"decrement is\",round(x,2)\n",
"print \"answer given in the book is wrong\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 7.15, Page number 7.5"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"number of people originally present is 12.0\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"aold=1; #first ratio term\n",
"bold=2; #second ratio term\n",
"anew=1; #first term of new ratio\n",
"bnew=3; #second term of new ratio\n",
"g=2; #number of gents left\n",
"l=2; #number of ladies left\n",
"\n",
"#Calculation\n",
"Nr=(g*bnew)-(anew*l);\n",
"Dr=bnew-(anew*l);\n",
"x=Nr/Dr; #factor\n",
"n=x*(aold+bold); #number of people originally present\n",
"\n",
"#Result\n",
"print \"number of people originally present is\",n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 7.16, Page number 7.5"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"number of each type of coin is 20.0 coins\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"c1=1; #coin value 1 rupee\n",
"c2=0.5; #coin value 50 paise\n",
"c3=0.25; #coin value 25 paise\n",
"t=35; #total amount(Rs)\n",
"\n",
"#Calculation\n",
"n=t/(c1+c2+c3); #number of each type of coin(coins)\n",
"\n",
"#Result\n",
"print \"number of each type of coin is\",n,\"coins\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 7.17, Page number 7.5"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"fraction of same ratio is 0.183673469388\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=3/7;\n",
"b=1/5;\n",
"c=7/15;\n",
"\n",
"#Calculation\n",
"x=a*b/c; #fraction of same ratio\n",
"\n",
"#Result\n",
"print \"fraction of same ratio is\",x"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 7.18, Page number 7.5"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"present age of C is 42.0 years\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"s=90; #sum of ages of A, B, C(years)\n",
"n=6; #number of years ago\n",
"a=1; #ratio term for age of A\n",
"b=2; #ratio term for age of B\n",
"c=3; #ratio term for age of C\n",
"\n",
"#Calculation\n",
"age=s-(n*c); #sum of ages of A, B, C 6 years ago(years)\n",
"C=c*age/(a+b+c); #age of C 6 years ago(years)\n",
"Cp=C+a+b+c; #present age of C(years)\n",
"\n",
"#Result\n",
"print \"present age of C is\",Cp,\"years\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 7.19, Page number 7.5"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"second number is 12.0\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"s=532; #sum of squares of 3 numbers\n",
"a=3; #first term of ratio\n",
"b=2; #second term of ratio\n",
"\n",
"#Calculation\n",
"n1=a*a; #first number\n",
"n2=a*b; #second number\n",
"n3=b*b; #third number\n",
"x2=s/((n1**2)+(n2**2)+(n3**2));\n",
"x=math.sqrt(x2); #factor\n",
"N2=n2*x; #second number\n",
"\n",
"#Result\n",
"print \"second number is\",N2"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 7.20, Page number 7.6"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"weight of wire is 188.0 kg\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"l1=60; #length of wire(m)\n",
"w1=80; #weight of wire(kg)\n",
"l2=141; #length of another wire(m)\n",
"\n",
"#Calculation\n",
"x=w1*l2/l1; #weight of wire(kg)\n",
"\n",
"#Result\n",
"print \"weight of wire is\",x,\"kg\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 7.21, Page number 7.6"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"value of a/bc : b/ca is 4\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"bc=1; #first term of ratio\n",
"ac=2; #second term of ratio\n",
"ab=3; #third term of ratio\n",
"\n",
"#Calculation\n",
"#abyb=ac/bc\n",
"a=ac;\n",
"b=bc;\n",
"result=(a**2)/(b**2); #value of a/bc : b/ca\n",
"\n",
"#Result\n",
"print \"value of a/bc : b/ca is\",int(result)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 7.23, Page number 7.6"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"number of 1 rupee coins is 5.0\n",
"number of 50 paise coins is 15.0\n",
"number of 25 paise coins is 25.0\n",
"number of 10 paise coins is 35.0\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"v1=1; #one rupee coin\n",
"v2=1/2; #50 paise coin\n",
"v3=1/4; #25 paise coin\n",
"v4=1/10; #10 paise coin\n",
"n1=1; #number of 1 rupee coins\n",
"n2=3; #number of 50 paise coins\n",
"n3=5; #number of 25 paise coins\n",
"n4=7; #number of 10 paise coins\n",
"s=22.25; #total amount(Rs)\n",
"\n",
"#Calculation\n",
"a=(v1*n1)+(v2*n2)+(v3*n3)+(v4*n4);\n",
"x=s/a; #factor\n",
"N1=x*n1; #number of 1 rupee coins\n",
"N2=x*n2; #number of 50 paise coins\n",
"N3=x*n3; #number of 25 paise coins\n",
"N4=x*n4; #number of 10 paise coins\n",
"\n",
"#Result\n",
"print \"number of 1 rupee coins is\",N1\n",
"print \"number of 50 paise coins is\",N2\n",
"print \"number of 25 paise coins is\",N3\n",
"print \"number of 10 paise coins is\",N4"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 7.24, Page number 7.7"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"the person should have atleast 57.0 pens\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"from fractions import gcd\n",
"\n",
"#Variable declaration\n",
"a=1/3;\n",
"b=1/4;\n",
"c=1/5;\n",
"d=1/6;\n",
"\n",
"#Calculation\n",
"l1=(1/a)*(1/b)/gcd(1/a,1/b);\n",
"l2=(1/c)*(1/d)/gcd(1/c,1/d);\n",
"l=l1*l2/gcd(l1,l2); #lcm of 3,4,5,6\n",
"A=a*l;\n",
"B=b*l;\n",
"C=c*l;\n",
"D=d*l;\n",
"p=A+B+C+D;\n",
"\n",
"#Result\n",
"print \"the person should have atleast\",p,\"pens\""
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.9"
}
},
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