path: root/Quantitative_Aptitude_for_Competitive_Examinations/Chapter9.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 9: Mixtures"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 9.1, Page number 9.4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "proportion to be mixed is 4\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "c1=9.5;      #cost of oil per kg(Rs)\n",
    "c2=10;       #cost of another oil(Rs)\n",
    "Cm=9.6;      #cost of mixture(Rs)\n",
    "\n",
    "#Calculation\n",
    "q1byq2=(c2-Cm)/(Cm-c1);     #proportion to be mixed\n",
    "\n",
    "#Result\n",
    "print \"proportion to be mixed is\",int(q1byq2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 9.2, Page number 9.4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "proportion to be mixed is 0.666666666667\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "c1=25;      #percentage of alcohol(%)\n",
    "c2=50;       #percentage of alcohol(%)\n",
    "Cm=40;      #alcohol strength(%)\n",
    "\n",
    "#Calculation\n",
    "q1byq2=(c2-Cm)/(Cm-c1);     #proportion to be mixed\n",
    "\n",
    "#Result\n",
    "print \"proportion to be mixed is\",q1byq2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 9.3, Page number 9.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "quantity of money lent at 8% is 400.0 Rs\n",
      "quantity of money lent at 10% is 600.0 Rs\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "c1=8;      #first part(%)\n",
    "c2=10;       #second part(%)\n",
    "Cm=9.2;      #yearly average(%)\n",
    "A=1000;      #amount(Rs)\n",
    "\n",
    "#Calculation\n",
    "q1=c2-Cm;\n",
    "q2=Cm-c1;     \n",
    "A1=q1*A/(q1+q2);      #quantity of money lent at 8%(Rs)\n",
    "A2=q2*A/(q1+q2);      #quantity of money lent at 10%(Rs)\n",
    "\n",
    "#Result\n",
    "print \"quantity of money lent at 8% is\",A1,\"Rs\"\n",
    "print \"quantity of money lent at 10% is\",A2,\"Rs\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 9.4, Page number 9.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "amount of water to be added is 5.0 litres\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "c1=0;      #pure milk(litres)\n",
    "c2=3.6;       #cost of pure milk(Rs)\n",
    "Cm=3;      #cost of mixture(Rs)\n",
    "\n",
    "#Calculation\n",
    "q1byq2=(Cm-c1)/(c2-Cm);     #amount of water to be added(litres)\n",
    "\n",
    "#Result\n",
    "print \"amount of water to be added is\",q1byq2,\"litres\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 9.5, Page number 9.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "amount of salt is 20.0 kg\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "c1=24;      #cost of salt(paise)\n",
    "c2=42;      #cost of salt(paise)\n",
    "c=40;       #cost of mixture(paise)\n",
    "e=25;       #efficiency(%) \n",
    "\n",
    "#Calculation\n",
    "Cm=c*100/(100+e);      #cost price of mixture(paise)\n",
    "q1byq2=(Cm-c1)/(c2-Cm);      #proportion to be mixed\n",
    "q=q1byq2*e;        #amount of salt(kg)\n",
    "\n",
    "#Result\n",
    "print \"amount of salt is\",q,\"kg\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 9.6, Page number 9.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "strength of alcohol is 16.6666666667 %\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=5;       #amount of alcohol solution(litres)\n",
    "p=20/100;    #percentage of solution\n",
    "\n",
    "#Calculation\n",
    "A=p*a;      #amount of alcohol(litre)\n",
    "S=A*100/(A+a);    #strength of alcohol(%)\n",
    "\n",
    "#Result\n",
    "print \"strength of alcohol is\",S,\"%\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 9.7, Page number 9.6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "amount of water to be added is 5.0 litres\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "p1=90/100;      #percentage of milk in mixture(%)\n",
    "p2=10/100;      #percentage of water in mixture(%)\n",
    "a=40;       #amount of mixture(litres)\n",
    "p_2=20;     #new percent of water(%)\n",
    "\n",
    "#Calculation\n",
    "A=(p1*a*p_2/(100-p_2))-(p2*a);     #amount of water to be added(litres)\n",
    "\n",
    "#Result\n",
    "print \"amount of water to be added is\",A,\"litres\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 9.8, Page number 9.6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "amount of pure milk is 25.0 litres\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "c1=0;      \n",
    "c2=3.0;      #cost of pure milk(Rs)\n",
    "e=20/100;       #efficiency(%) \n",
    "\n",
    "#Calculation\n",
    "Cm=c2/(1+e);    #CP of mixture(Rs)\n",
    "q1byq2=(Cm-c1)/(c2-Cm);      #proportion to be mixed\n",
    "A=q1byq2**2;        #amount of pure milk(litres)\n",
    "\n",
    "#Result\n",
    "print \"amount of pure milk is\",A,\"litres\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 9.9, Page number 9.6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "selling price of mixture is Rs 7.04 per kg\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a1=6;     #amount of tea(kg)\n",
    "p1=6;     #cost of tea(Rs)\n",
    "a2=4;     #amount of tea(kg)\n",
    "p2=7;     #cost of tea(Rs)\n",
    "p=10/100;    #profit(p)\n",
    "\n",
    "#Calculation\n",
    "cp=((a1*p1)+(a2*p2))/(a1+a2);       #cost price of mixture(Rs)\n",
    "sp=(1+p)*cp;           #selling price of mixture(Rs)\n",
    "\n",
    "#Result\n",
    "print \"selling price of mixture is Rs\",sp,\"per kg\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 9.10, Page number 9.6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "strength of acid in mixture is 60.0 %\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "p1=20;    #percentage of sulphuric acid(%)\n",
    "q1=5;     #amount of acid(litres)\n",
    "p2=100;   #percentage of pure sulphuric acid(%)\n",
    "q2=5;     #amount of acid(litres)\n",
    "\n",
    "#Calculation\n",
    "s=((p1*q1)+(p2*q2))/(q1+q2);    #strength of acid in mixture(%)\n",
    "\n",
    "#Result\n",
    "print \"strength of acid in mixture is\",s,\"%\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 9.11, Page number 9.6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "cost price of 1st liquid is Rs 10.8 per litre\n",
      "cost price of 2nd liquid is Rs 8.8 per litre\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "q1=3\n",
    "q2=2;        \n",
    "c=11;     #cost at which mixture is sold(Rs)\n",
    "p=10/100;     #profit(%)\n",
    "\n",
    "#Calculation\n",
    "Cm=c/(1+p);    #cost price of mixture(Rs)\n",
    "x=((q2*Cm)+(q1*Cm)+(q2*q2))/(q1+q2);      #cost price of 1st liquid(Rs)\n",
    "x2=x-q2;      #cost price of 2nd liquid(Rs)\n",
    "\n",
    "#Result\n",
    "print \"cost price of 1st liquid is Rs\",x,\"per litre\"\n",
    "print \"cost price of 2nd liquid is Rs\",x2,\"per litre\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 9.12, Page number 9.7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "alcohol and water are in the proportion of 1.4\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=2;\n",
    "b=1;       #proportion of 1st mixture of alcohol and water\n",
    "x=1;\n",
    "y=1;       #proportion of 2nd mixture of alcohol and water\n",
    "\n",
    "#Calculation\n",
    "q1=(a/(a+b))+(x/(x+y));      #quantity of alcohol in 3rd glass\n",
    "q2=(b/(a+b))+(y/(x+y));      #quantity of water in 3rd glass\n",
    "\n",
    "#Result\n",
    "print \"alcohol and water are in the proportion of\",q1/q2 "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 9.13, Page number 9.7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "gain made on sale of 5 quintals is Rs 110.0\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "c1=2.10;      #cost price of coffee(Rs)\n",
    "q1=15;     #quantity of coffee(parts)\n",
    "c2=0.98;   #cost price of chicory(Rs)\n",
    "q2=1;      #quantity of chicory(part)\n",
    "s=2.25;    #selling price per kg(Rs)\n",
    "a=500;     #amount(kg)\n",
    "\n",
    "#Calculation\n",
    "Cm=((c1*q1)+(c2*q2))/(q1+q2);     #cost price of mixture(Rs)\n",
    "p=(s-Cm)*a;             #gain made on sale of 5 quintals(Rs)\n",
    "\n",
    "#Result\n",
    "print \"gain made on sale of 5 quintals is Rs\",p"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 9.14, Page number 9.8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "percentage of alcohol is 28.0 %\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "qa=35;       #percentage of alcohol by weight\n",
    "qw=25;     #weight of water(gms)\n",
    "m=100;     #total mixture(g)\n",
    "\n",
    "#Calculation\n",
    "p=qa*100/(m+qw);      #percentage of alcohol(%)\n",
    "\n",
    "#Result\n",
    "print \"percentage of alcohol is\",p,\"%\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 9.15, Page number 9.8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "quantity of the butt stolen is 0.57\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "Cm=24;     #strength of butt(%)\n",
    "c1=18;     #percentage of spirit(%)\n",
    "c2=32;     #percentage of spirit(%)\n",
    "\n",
    "#Calculation\n",
    "q1=Cm-c1;    #quantity of 32% spirit\n",
    "q2=c2-Cm;    #quantity of 18% spirit\n",
    "f=q2/(q1+q2);     #quantity of the butt stolen\n",
    "\n",
    "#Result\n",
    "print \"quantity of the butt stolen is\",round(f,2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 9.16, Page number 9.8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "quantity of water added is 22.0 litres\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "m=66;    #mixture of milk(litres)\n",
    "a=5;\n",
    "b=1;     #ratio of milk and water\n",
    "x=5;\n",
    "y=3;     #new ratio  \n",
    "\n",
    "#Calculation\n",
    "x1=a*m*y/(a+b);\n",
    "x2=a*m/(x+b);\n",
    "x=(x1-x2)/a;     #quantity of water added(litres)\n",
    "\n",
    "#Result\n",
    "print \"quantity of water added is\",x,\"litres\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 9.17, Page number 9.8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "amount of dry fruit obtained is 35.0 kg\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "qw1=72/100;       #content of water in fresh fruit(%)\n",
    "a=100;     #amount of fresh fruit(kg)\n",
    "qw2=20/100;       #content of water in dry fruit(%)\n",
    "\n",
    "#Calculation\n",
    "x=(1-qw1)*a/(1-qw2);       #amount of dry fruit obtained(kg)\n",
    "\n",
    "#Result\n",
    "print \"amount of dry fruit obtained is\",x,\"kg\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 9.18, Page number 9.8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "quantity of fresh water to be added is 40.0 kg\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "qs=5/100;     #content of salt by water(%)\n",
    "a=60;         #amount of sea water(kg)\n",
    "q=3;      #content of salt in solution(%)\n",
    "\n",
    "#Calculation\n",
    "x=((qs*a*100)-(q*a))/q;         #quantity of fresh water to be added(kg)\n",
    "\n",
    "#Result\n",
    "print \"quantity of fresh water to be added is\",x,\"kg\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 9.19, Page number 9.9"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "amount of first alloy is 7.0 kg\n",
      "amount of second alloy is 21.0 kg\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "qa=1;     #copper in 1st alloy\n",
    "qb=1;     #copper in 2nd alloy\n",
    "x=3;\n",
    "y=4;      #ratio of copper to zinc\n",
    "a=5;\n",
    "b=2;      #ration of copper to zinc in new alloy\n",
    "q=28;     #quantity of new alloy(kg) \n",
    "\n",
    "#Calculation\n",
    "Cm=qa/(qa+qb);      #copper in new alloy\n",
    "c1=x/(x+y);         #copper in 2nd alloy\n",
    "c2=a/(a+b);         #copper in 1st alloy\n",
    "q1=(Cm-c1);\n",
    "q2=(c2-Cm);\n",
    "a1=q1*q/(q1+q2);    #amount of 1st alloy(kg)\n",
    "a2=q-a1;            #amount of second alloy(kg)\n",
    "\n",
    "#Result\n",
    "print \"amount of first alloy is\",a1,\"kg\"\n",
    "print \"amount of second alloy is\",a2,\"kg\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 9.20, Page number 9.9"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "weight of new alloy is 35.0 kg\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a1=4;\n",
    "b1=1;       #relation of copper and zinc\n",
    "a2=1;\n",
    "b2=3;       #relation of copper and zinc\n",
    "a3=3;\n",
    "b3=2;       #ratio of copper to zinc \n",
    "q1=10;      #amount of 1st alloy(kg)\n",
    "q2=16;      #amount of 2nd alloy(kg)\n",
    "\n",
    "#Calculation\n",
    "c1=a1*q1/(a1+b1);      #copper in 1st alloy\n",
    "c2=a2*q2/(a2+b2);      #copper in 2nd alloy\n",
    "x=(a3*(q1+q2))-((a3+b3)*(c1+c2));       \n",
    "w=(x/2)+q1+q2;      #weight of new alloy(kg)\n",
    "\n",
    "#Result\n",
    "print \"weight of new alloy is\",w,\"kg\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 9.21, Page number 9.10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "number of boys is 33.0\n",
      "number of girls is 12.0\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=39;     #amount(Rs)\n",
    "s=45;     #number of boys and girls\n",
    "c1=50/100;    #amount girl gets(Rs)\n",
    "c2=1;         #amount boy gets(Rs)\n",
    "\n",
    "#Calculation\n",
    "Cm=a/s;\n",
    "qb=(Cm-c1);     #number of boys in ratio\n",
    "qg=(c2-Cm);     #number of girls in ratio\n",
    "b=qb*s/(qb+qg);     #number of boys\n",
    "g=s-b;              #number of girls\n",
    "\n",
    "#Result\n",
    "print \"number of boys is\",b\n",
    "print \"number of girls is\",g"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 9.22, Page number 9.10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "quantity of mixture released is 2.0 litres\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "co=9/100;      #content of oxygen\n",
    "vo=16/100;     #volume of oxygen\n",
    "q=8;       #quantity of cylinder(litre)\n",
    "\n",
    "#Calculation\n",
    "r=math.sqrt(co*q/(vo*q));\n",
    "R=q*(1-r);     #quantity of mixture released(litres)\n",
    "\n",
    "#Result\n",
    "print \"quantity of mixture released is\",R,\"litres\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 9.23, Page number 9.10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "amount of milk left is 72.9 kg\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "x0=100;     #original amount of milk(kg)\n",
    "xr=10;      #amount of milk removed(kg)\n",
    "n=3;        #number of operations\n",
    "\n",
    "#Calculation\n",
    "a=x0*(1-(xr/x0))**n;       #amount of milk left(kg)\n",
    "\n",
    "#Result\n",
    "print \"amount of milk left is\",a,\"kg\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 9.24, Page number 9.11"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ratio of dettol and water is 0.25\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "x0=1;     #quantity of dettol(litre)\n",
    "xr=1/3;      #quantity of dettol removed(litre)\n",
    "n=4;        #number of operations\n",
    "\n",
    "#Calculation\n",
    "Aa=(1-(xr/x0))**n;       #amount of dettol left(litre)\n",
    "Ba=1-Aa;                 #amount of water left(litre)\n",
    "r=Aa/Ba;                 #ratio of dettol and water \n",
    "\n",
    "#Result\n",
    "print \"ratio of dettol and water is\",round(r,2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 9.25, Page number 9.12"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "part of the mixture taken out is 0.2\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a1=5;      #parts of after shave lotion\n",
    "b1=3;      #parts of water\n",
    "Al=1/2;               #amount of after shave lotion\n",
    "\n",
    "#Calculation\n",
    "Ap=a1/(a1+b1);      #amount of after shave lotion present\n",
    "R=1-(Al/Ap);        #part of the mixture taken out\n",
    "\n",
    "#Result\n",
    "print \"part of the mixture taken out is\",R"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 9.26, Page number 9.12"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "three kinds of rice are mixed in the ratio 11.0 : 77.0 : 7.0\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "c1=12;       #cost price of 1st variety(Rs)\n",
    "c2=14.40;    #cost price of 2nd variety(Rs)\n",
    "c3=17.40;    #cost price of 3rd variety(Rs)\n",
    "Cm=14.10;    #cost price of mixture(Rs)\n",
    "f=11.11;     #factor to be rounded off\n",
    "\n",
    "#Calculation\n",
    "q1=(c2-Cm)*(c3-Cm)*f;     #quantity of 1st variety(kg)\n",
    "q2=(Cm-c1)*(c3-Cm)*f;     #quantity of 2nd variety(kg)\n",
    "q3=(c2-Cm)*(Cm-c1)*f;     #quantity of 3rd variety(kg)\n",
    "\n",
    "\n",
    "#Result\n",
    "print \"three kinds of rice are mixed in the ratio\",round(q1),\":\",round(q2),\":\",round(q3)"
   ]
  }
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