{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#8: Partnership and Share"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 8.1, Page number 8.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "investment of A is 5000.0 Rs\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "A=12000;     #investment of A and B(Rs)\n",
    "P=1800;     #profit(Rs)\n",
    "Pa=750;     #profit of A(Rs)\n",
    "\n",
    "#Calculation\n",
    "ratio=Pa/(P-Pa);     #ratio of investments\n",
    "Ia=Pa*A/P;      #investment of A(Rs)\n",
    "\n",
    "#Result\n",
    "print \"investment of A is\",Ia,\"Rs\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 8.2, Page number 8.2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "profit share of A is 1500.0 Rs\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "Ca=10000;    #capital of A(Rs)\n",
    "na=12;    #number of years\n",
    "nb=4;     #number of years\n",
    "Cb=5000;    #capital of B(Rs)\n",
    "P=2000;    #total profit(Rs)\n",
    "\n",
    "#Calculation\n",
    "a=Ca*na;\n",
    "b=Cb*(na-nb);\n",
    "r=a/b;     #ratio of profits\n",
    "Pa=a*P/(a+b);     #profit share of A(Rs)\n",
    "\n",
    "#Result\n",
    "print \"profit share of A is\",Pa,\"Rs\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 8.3, Page number 8.2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "profit of A is 57.0 Rs\n",
      "profit of B is 60.0 Rs\n",
      "profit of C is 63.0 Rs\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "Ia=380;     #investment of A(Rs)\n",
    "Ib=400;     #investment of B(Rs)\n",
    "Ic=420;     #investment of C(Rs)\n",
    "P=180;     #net profit(Rs)\n",
    "\n",
    "#Calculation\n",
    "I=Ia+Ib+Ic;     #total investment(Rs)\n",
    "Pa=Ia*P/I;     #profit of A(Rs)\n",
    "Pb=Ib*P/I;     #profit of B(Rs)\n",
    "Pc=Ic*P/I;     #profit of C(Rs)\n",
    "\n",
    "#Result\n",
    "print \"profit of A is\",Pa,\"Rs\"\n",
    "print \"profit of B is\",Pb,\"Rs\"\n",
    "print \"profit of C is\",Pc,\"Rs\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 8.4, Page number 8.2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "profit of A is 64.0 Rs\n",
      "profit of B is 76.5 Rs\n",
      "profit of C is 67.5 Rs\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "Ca=320*4;    #contribution of A for 4 months(Rs)\n",
    "Cb=510*3;    #contribution of B for 3 months(Rs)\n",
    "Cc=270*5;    #contribution on C for 5 months(Rs)\n",
    "P=208;     #net profit(Rs)\n",
    "\n",
    "#Calculation\n",
    "C=Ca+Cb+Cc;     #contribution of A,B,C(Rs)\n",
    "Pa=Ca*P/C;     #profit of A(Rs)\n",
    "Pb=Cb*P/C;     #profit of B(Rs)\n",
    "Pc=Cc*P/C;     #profit of C(Rs)\n",
    "\n",
    "#Result\n",
    "print \"profit of A is\",Pa,\"Rs\"\n",
    "print \"profit of B is\",Pb,\"Rs\"\n",
    "print \"profit of C is\",Pc,\"Rs\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 8.5, Page number 8.2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "profit of B is 420.0 Rs\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "C=8200;    #total capital(Rs)\n",
    "a=1000;\n",
    "b=2000;\n",
    "Cb=(C-(b+a+a))/3;      #capital of B(Rs)\n",
    "P=2460;     #total profit(Rs)\n",
    "\n",
    "#Calculation\n",
    "Pb=Cb*P/C;    #profit of B(Rs)\n",
    "\n",
    "#Result\n",
    "print \"profit of B is\",Pb,\"Rs\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 8.6, Page number 8.3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "C must pay Rs 10.0 to A\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "m=50;     #amount with each person(Rs)\n",
    "mA=20;    #amount left with A(Rs)\n",
    "mB=30;    #amount left with B(Rs)\n",
    "mC=40;    #amount left with C(Rs)\n",
    "\n",
    "#Calculation\n",
    "Ms=m*3;     #total amount started with(Rs)\n",
    "Mr=mA+mB+mC;    #total amount ending with(Rs)\n",
    "M=Mr/3;        #amount each person must have(Rs)\n",
    "Cm=mC-M;      #C must pay(Rs)\n",
    "\n",
    "#Result\n",
    "print \"C must pay Rs\",Cm,\"to A\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 8.7, Page number 8.3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "share of C is 240.0 Rs\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=1290;    #amount(Rs)\n",
    "A=3;    #value of A in the ratio A:B\n",
    "B1=2;   #value of B in the ratio A:B \n",
    "B2=7;   #value of B in the ratio B:C\n",
    "C1=4;   #value of C in the ratio B:C\n",
    "\n",
    "#Calculation\n",
    "#inorder to make the value of B in the ratios same, multiply by B2\n",
    "A=A*B2;\n",
    "B=B1*B2;\n",
    "C=C1*B1;     #new values of the ratio A:B:C\n",
    "Sc=C*a/(A+B+C);    #share of C(Rs)\n",
    "\n",
    "#Result\n",
    "print \"share of C is\",Sc,\"Rs\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 8.8, Page number 8.3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "balance profit of B is 360.0 Rs\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "A=390;    #amount A receives(Rs)\n",
    "Ap=10*12;    #profit for A(Rs)\n",
    "Ia=3000;    #investment of A(Rs)\n",
    "Ib=4000;    #investment of B(Rs)\n",
    "\n",
    "#Calculation\n",
    "Ba=A-Ap;    #balance profit of A(Rs)\n",
    "Bb=Ba*Ib/Ia;     #balance profit of B(Rs)\n",
    "\n",
    "#Result\n",
    "print \"balance profit of B is\",Bb,\"Rs\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 8.9, Page number 8.3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "total amount of money is 200 Rs\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "BplusC=100;     #amount with B and C(Rs)\n",
    "AplusC=150;      #amount with A and C(Rs)\n",
    "\n",
    "#Calculation\n",
    "B=AplusC-BplusC;     #amount with B(Rs)\n",
    "ABC=AplusC+B;        #total amount of money(Rs)\n",
    "\n",
    "#Result\n",
    "print \"total amount of money is\",ABC,\"Rs\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 8.10, Page number 8.4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "profit share of A is 330.0 Rs\n",
      "profit share of B is 430.0 Rs\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "A=760;    #amount(Rs)\n",
    "Ar=4;     #part of A in ratio\n",
    "Br=5;     #part of B in ratio\n",
    "At=3;     #time for A(months)\n",
    "AT=10-3;   #ending time(months)\n",
    "\n",
    "#Calculation\n",
    "MEI_A=(Ar*At)+(AT*Ar*At/Ar);    #monthly equivalent investment of A\n",
    "MEI_B=(Br*At)+(AT*Br*Ar/Br);    #monthly equivalent investment of B\n",
    "PA=MEI_A*A/(MEI_A+MEI_B);     #profit share of A(Rs)\n",
    "PB=MEI_B*A/(MEI_A+MEI_B);     #profit share of B(Rs)\n",
    "\n",
    "#Result\n",
    "print \"profit share of A is\",PA,\"Rs\"\n",
    "print \"profit share of B is\",PB,\"Rs\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 8.11, Page number 8.4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "payment for rent by A is 8550.0 Rs\n",
      "payment for rent by B is 5950.0 Rs\n",
      "payment for rent by C is 9200.0 Rs\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "Fd_A=27;     #floppy disks of A\n",
    "Ad=19;    #number of days for A\n",
    "Fd_B=21;  #floppy disks of B\n",
    "Bd=17;    #number of days for B\n",
    "Fd_C=24;  #floppy disks of C\n",
    "Cd=23;    #number of days for C\n",
    "am=23700;    #amount(Rs)\n",
    "\n",
    "#Calculation\n",
    "A=Fd_A*Ad;    #A's floppy days\n",
    "B=Fd_B*Bd;    #B's floppy days\n",
    "C=Fd_C*Cd;    #C's floppy days\n",
    "PA=A*am/(A+B+C);    #payment for rent by A(Rs)\n",
    "PB=B*am/(A+B+C);    #payment for rent by B(Rs)\n",
    "PC=C*am/(A+B+C);    #payment for rent by C(Rs)\n",
    "\n",
    "#Result\n",
    "print \"payment for rent by A is\",PA,\"Rs\"\n",
    "print \"payment for rent by B is\",PB,\"Rs\"\n",
    "print \"payment for rent by C is\",PC,\"Rs\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 8.12, Page number 8.4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "capital of A is 3000.0 Rs\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "S=1000;     #share of A(Rs)\n",
    "IA=8;     #investment of A(months)\n",
    "IB=12;     #investment of B(months)\n",
    "PA=PB=1;  \n",
    "\n",
    "#Calculation\n",
    "CA=(PA/PB)*S*(IB/(IA/2));        #capital of A(Rs)\n",
    "\n",
    "#Result\n",
    "print \"capital of A is\",CA,\"Rs\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 8.13, Page number 8.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "total profit is 1000.0 Rs\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",
    "Sa=4000;     #A's share(s)\n",
    "Sb=5000;     #B's share(Rs)\n",
    "Sc=6000;     #C's share(Rs)\n",
    "r=1000;    #ratio fraction\n",
    "p=75/100;  #profit percentage(%)\n",
    "P=25/100;\n",
    "A=100;    #A gets less(Rs)\n",
    "\n",
    "#Calculation\n",
    "TP=((Sa/r)+(Sb/r)+(Sc/r))/p;     #total profit\n",
    "As=(Sa/r)+(P*TP);         #share of A\n",
    "Bs=Sb/r;         #share of B\n",
    "Cs=Sc/r;         #share of C\n",
    "x=A/((Bs+Cs)-As);\n",
    "Tp=TP*x;         #total profit(Rs)\n",
    "\n",
    "#Result\n",
    "print \"total profit is\",Tp,\"Rs\"\n",
    "print \"answer given in the book is wrong\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 8.14, Page number 8.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "total profit is 393.75 Rs\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "AP40=1250;     #A's 40% profit(Rs)\n",
    "BP40=850;      #B's 40% profit(Rs)\n",
    "A=30;    #amount received more(Rs)\n",
    "p=60/100;   #distributed profit(%)\n",
    "\n",
    "#Calculation\n",
    "R=(AP40+BP40)/(AP40-BP40);      #applying componendo dividendo\n",
    "P=R*A/(1-p);         #total profit(Rs)\n",
    "\n",
    "#Result\n",
    "print \"total profit is\",P,\"Rs\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 8.15, Page number 8.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "share of A is 100.0 Rs\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "CA=1/6;       #capital of A\n",
    "CB=1/3;       #capital of B\n",
    "P=2300;     #total profit(Rs)\n",
    "\n",
    "#Calculation\n",
    "CC=1-CA-CB;    #capital of C\n",
    "PA=CA*CA*12;   #A's profit\n",
    "PB=CB*CB*12;   #B's profit\n",
    "PC=CC*12;      #C's profit\n",
    "SA=PA*P/(PA+PB+PC);       #share of A(Rs)\n",
    "\n",
    "#Result\n",
    "print \"share of A is\",SA,\"Rs\""
   ]
  }
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