{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 11: Time and Work"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 11.1, Page number 11.4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A and B can do the job together in 12.0 days\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "t1=20;      #number of days A can do a job\n",
    "t2=30;      #number of days B can do a job\n",
    "\n",
    "#Calculation\n",
    "T=t1*t2/(t1+t2);     #number of days for A and B to do the job together\n",
    "\n",
    "#Result\n",
    "print \"A and B can do the job together in\",T,\"days\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 11.2, Page number 11.4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A can do the job in 21.0 days\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "t1=28;     #number of days B can do a job\n",
    "T=12;      #number of days for A and B to do the job together\n",
    "\n",
    "#Calculation\n",
    "t2=T*t1/(t1-T);     #number of days A can do a job\n",
    "\n",
    "#Result\n",
    "print \"A can do the job in\",t2,\"days\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 11.3, Page number 11.4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "work done by A, B and C together is 10.0 days\n",
      "work done by A alone is 30.0 days\n",
      "work done by B alone is 20.0 days\n",
      "work done by C alone is 60.0 days\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "from fractions import gcd\n",
    "\n",
    "#Variable declaration\n",
    "T1=12;      #work done by A and B together(days)\n",
    "T2=15;      #work done by C and B together(days)\n",
    "T3=20;      #work done by A and C together(days)\n",
    "\n",
    "#Calculation\n",
    "l1=T1*T2/gcd(T1,T2);     #lcm of T1 and T2\n",
    "L=l1*T3/gcd(l1,T3);     #lcm of the given 3 numbers\n",
    "a=L/T1;\n",
    "b=L/T2;\n",
    "c=L/T3;\n",
    "T=2*L/(a+b+c);         #work done by A, B and C together(days)\n",
    "Ta=2*L/(a-b+c);         #work done by A alone(days)\n",
    "Tb=2*L/(a+b-c);         #work done by B alone(days)\n",
    "Tc=2*L/(-a+b+c);         #work done by C alone(days)\n",
    "\n",
    "#Result\n",
    "print \"work done by A, B and C together is\",T,\"days\"\n",
    "print \"work done by A alone is\",Ta,\"days\"\n",
    "print \"work done by B alone is\",Tb,\"days\"\n",
    "print \"work done by C alone is\",Tc,\"days\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 11.4, Page number 11.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "total work is finished in 8.0 days\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "Ta=10;     #alone time of A(days)\n",
    "TB=3;      #number of days B worked(days)\n",
    "Tb=15;     #alone time of B(days)\n",
    "\n",
    "#Calculation\n",
    "T=Ta*(1-(TB/Tb));        #total work finished(days)\n",
    "\n",
    "#Result\n",
    "print \"total work is finished in\",T,\"days\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 11.5, Page number 11.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "total work is finished in 15.0 days\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "from fractions import gcd\n",
    "\n",
    "#Variable declaration\n",
    "Ta=20;     #alone time of A(days)\n",
    "Tb=30;     #alone time of B(days)\n",
    "a=5;       #number of days A leaves(days)\n",
    "\n",
    "#Calculation\n",
    "L=Ta*Tb/gcd(Ta,Tb);     #lcm of T1 and T2\n",
    "l1=L/Ta;\n",
    "l2=L/Tb;\n",
    "T=(L+(l1*a))/(l1+l2);     #total work finished(days)\n",
    "\n",
    "#Result\n",
    "print \"total work is finished in\",T,\"days\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 11.6, Page number 11.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "total work is finished in 8.72727272727 days\n",
      "B worked for 2.72727272727 days\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "from fractions import gcd\n",
    "\n",
    "#Variable declaration\n",
    "Ta=10;     #alone time of A(days)\n",
    "Tb=12;     #alone time of B(days)\n",
    "a=6;       #number of days after A started(days)\n",
    "\n",
    "#Calculation\n",
    "L=T1*T2/gcd(T1,T2);     #lcm of T1 and T2\n",
    "l1=L/Ta;\n",
    "l2=L/Tb;\n",
    "T=(L+(l1*a))/(l1+l2);     #total work finished(days)\n",
    "TB=T-a;         #number of days B worked for(days)\n",
    "\n",
    "#Result\n",
    "print \"total work is finished in\",T,\"days\"\n",
    "print \"B worked for\",TB,\"days\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 11.7, Page number 11.6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "number of days to complete the job is 10.0 days\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "M1=1;     #number of men\n",
    "E1=1;     #efficiency of anil\n",
    "D1=8;     #number of days worked(days)\n",
    "E=60/100;    #efficiency of rakesh(%)\n",
    "P1=1/3;      #part of work done by anil\n",
    "M2=1;     #number of men\n",
    "\n",
    "#Calculation\n",
    "E2=(M1*M2)+(E1*E);      #efficiency\n",
    "P2=1-P1;     #part of work done by rakesh\n",
    "D2=M1*E1*D1*P2/(P1*E2);     #number of days to complete the job(days)\n",
    "\n",
    "#Result\n",
    "print \"number of days to complete the job is\",D2,\"days\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 11.8, Page number 11.6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "time taken for A to complete the job is 6 1/4 days\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "from fractions import Fraction\n",
    "\n",
    "#Variable declaration\n",
    "T1=5;      #work done by A and B together(days)\n",
    "T=1;        #total job done\n",
    "eB=1/3;     #efficiency of B\n",
    "\n",
    "#Calculation\n",
    "t=T-(T/T1);   \n",
    "tA=T1*(1/t);     #time taken for A to complete the job(days)\n",
    "x=tA-int(tA);\n",
    "\n",
    "#Result\n",
    "print \"time taken for A to complete the job is\",int(tA),Fraction(x),\"days\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 11.9, Page number 11.6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A can finish in 2.0 days\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "M1=1;     #number of men\n",
    "D1=12;     #number of days worked(days)\n",
    "M2=1;     #number of men\n",
    "W1=3/4;    #work done by A\n",
    "W2=1/8;    #part of work done\n",
    "\n",
    "#Calculation\n",
    "d=M1*D1*W2/(W1*M2);     #number of days for A(days)\n",
    "\n",
    "#Result\n",
    "print \"A can finish in\",d,\"days\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 11.10, Page number 11.7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "total work is finished in 7.0 days\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "from fractions import gcd\n",
    "\n",
    "#Variable declaration\n",
    "Ta=10;     #alone time of A(days)\n",
    "Tb=12;     #alone time of B(days)\n",
    "Tc=15;     #alone time of C(days)\n",
    "a=2;       #number of days after A started(days)\n",
    "b=3;       #number of days before the work finished(days)\n",
    "\n",
    "#Calculation\n",
    "L1=Ta*Tb/gcd(Ta,Tb);     #lcm of Ta and Tb\n",
    "L=L1*Tc/gcd(L1,Tc);      #lcm of all the three\n",
    "l1=L/Ta;\n",
    "l2=L/Tb;\n",
    "l3=L/Tc;\n",
    "r=1-a/Ta;\n",
    "T=((r*L)+Tc)/(l2+l3);     #total work finished(days)\n",
    "TB=T-a;         #number of days B worked for(days)\n",
    "\n",
    "#Result\n",
    "print \"total work is finished in\",T,\"days\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 11.11, Page number 11.7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A left after 3.0 days\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "from fractions import gcd\n",
    "\n",
    "#Variable declaration\n",
    "T1=15;     #alone time of A(days)\n",
    "T2=10;     #alone time of B(days)\n",
    "a=5;       #number of days for B to finish(days)\n",
    "\n",
    "#Calculation\n",
    "L=T1*T2/gcd(T1,T2);     #lcm of T1 and T2\n",
    "l1=L/T1;\n",
    "l2=L/T2;\n",
    "x=(L-(l2*a))/(l1+l2);     #A left after days(days)\n",
    "\n",
    "#Result\n",
    "print \"A left after\",x,\"days\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 11.12, Page number 11.7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "C can do it alone in 25.0 days\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "T1=12;     #alone time of A(days)\n",
    "T2=15;     #alone time of B(days)\n",
    "T=2;       #number of days they work together(days)\n",
    "t=5;       #number of days work is completed(days)\n",
    "\n",
    "#Calculation\n",
    "Ta=(1+T+t)*(1/T1);      #A's amount of work\n",
    "Tb=T*(1/T2);       #B's amount of work\n",
    "T3=1-(Ta+Tb);\n",
    "t3=t/T3;         #C can do it in(days)\n",
    "\n",
    "#Result\n",
    "print \"C can do it alone in\",t3,\"days\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 11.13, Page number 11.7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "amount received by C is 5.33 Rs\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "from fractions import gcd\n",
    "\n",
    "#Variable declaration\n",
    "p=25;     #amount paid(Rs)\n",
    "A=32;     #number of days for A(days)\n",
    "B=20;     #number of days for B(days)\n",
    "C=12;     #number of days for C(days)\n",
    "D=24;     #number of days for B(days)\n",
    "\n",
    "#Calculation\n",
    "l1=A*B/gcd(A,B);     #lcm of A and B\n",
    "l2=C*D/gcd(C,D);     #lcm of C and D\n",
    "L=l1*l2/gcd(l1,l2);   #LCM of A,B,C and D\n",
    "a=L/A;\n",
    "b=L/B;\n",
    "c1=(1/C)-(1/B);\n",
    "c=L*c1;\n",
    "d=L/D;\n",
    "Cs=c*p/(a+b+c+d);     #amount received by C(Rs)\n",
    "\n",
    "#Result\n",
    "print \"amount received by C is\",round(Cs,2),\"Rs\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 11.14, Page number 11.8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "time taken to finish the job if A starts the work is 5.8 days\n",
      "time taken to finish the job if B starts the work is 5.86 days\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "tA=5;     #work for A alone(days)\n",
    "tB=7;     #work for B alone(days)\n",
    "\n",
    "#Calculation\n",
    "p=round(tA*tB/(tA+tB));    #nearest integer value\n",
    "Ta=((tA*tB)+(p*(tA-tB)))/tA;     #time taken to finish the job if A starts the work(days)\n",
    "Tb=((tA*tB)-(p*(tA-tB)))/tB;     #time taken to finish the job if B starts the work(days)\n",
    "\n",
    "#Result\n",
    "print \"time taken to finish the job if A starts the work is\",Ta,\"days\"\n",
    "print \"time taken to finish the job if B starts the work is\",round(Tb,2),\"days\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Example number 11.15, Page number 11.8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "job is finished in 15.0 days\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "tA=20;     #number of days for A(days)\n",
    "tB=30;     #number of days for B(days)\n",
    "tC=60;     #number of days for C(days)\n",
    "da=3;      #help done by A\n",
    "db=1;\n",
    "dc=1;\n",
    "\n",
    "#Calculation\n",
    "t=(da/tA)+(db/tB)+(dc/tC);\n",
    "T=da/t;       #job is finished in(days)\n",
    "\n",
    "#Result\n",
    "print \"job is finished in\",T,\"days\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 11.16, Page number 11.8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "job is finished in 30.0 days\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "K=3;\n",
    "l=80;     #number of days\n",
    "\n",
    "#Calculation\n",
    "T=K*l/((K**2)-1);     #job is finished in(days)\n",
    "\n",
    "#Result\n",
    "print \"job is finished in\",T,\"days\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 11.17, Page number 11.9"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "time taken if they work together is 12.0 days\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "tA=20;     #work by skilled men(days)\n",
    "tB=30;     #work by boys(days)\n",
    "\n",
    "#Calculation\n",
    "T=tA*tB/(tA+tB);       #time taken if they work together(days) \n",
    "\n",
    "#Result\n",
    "print \"time taken if they work together is\",T,\"days\""
   ]
  }
 ],
 "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"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}