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diff --git a/Quantitative_Aptitude_for_Competitive_Examinations/Chapter10.ipynb b/Quantitative_Aptitude_for_Competitive_Examinations/Chapter10.ipynb new file mode 100755 index 00000000..e80ad105 --- /dev/null +++ b/Quantitative_Aptitude_for_Competitive_Examinations/Chapter10.ipynb @@ -0,0 +1,659 @@ +{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# 10: Chain Rule"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 10.1, Page number 10.2"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "number of days is 80.0\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "N1=120; #number of men\n",
+ "N2=150; #number of men\n",
+ "D1=100; #number of days\n",
+ "\n",
+ "#Calculation\n",
+ "D2=N1*D1/N2; #number of days\n",
+ "\n",
+ "#Result\n",
+ "print \"number of days is\",D2"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 10.2, Page number 10.2"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "number of men is 15.0\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "N1=18; #number of men\n",
+ "D1=8; #number of days\n",
+ "D2=6; #number of days\n",
+ "R1=5; #number of hours\n",
+ "R2=8; #number of hours\n",
+ "\n",
+ "#Calculation\n",
+ "N2=N1*D1*R1/(D2*R2); #number of men\n",
+ "\n",
+ "#Result\n",
+ "print \"number of men is\",N2"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 10.3, Page number 10.2"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "number of days is 10.0\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "N1=1000; #number of men\n",
+ "D1=12; #number of days\n",
+ "N2=200; #number of men joined\n",
+ "\n",
+ "#Calculation\n",
+ "D2=N1*D1/(N1+N2); #number of days\n",
+ "\n",
+ "#Result\n",
+ "print \"number of days is\",D2"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 10.4, Page number 10.3"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "number of acres is 72.0\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "N1=4; #number of men\n",
+ "D1=30; #number of days\n",
+ "D2=12; #number of days\n",
+ "W1=40; #number of acres\n",
+ "N2=18; #number of men\n",
+ "\n",
+ "#Calculation\n",
+ "W2=N2*D2*W1/(D1*N1); #number of acres\n",
+ "\n",
+ "#Result\n",
+ "print \"number of acres is\",W2"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 10.5, Page number 10.3"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "number of days is 6.0\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "N1=12; #number of men\n",
+ "D1=25; #number of days\n",
+ "N2=20; #number of men\n",
+ "W1=100*3*0.5; #volume of wall\n",
+ "W2=60*4*0.25; #volume of wall\n",
+ "\n",
+ "#Calculation\n",
+ "D2=N1*D1*W2/(W1*N2); #number of days\n",
+ "\n",
+ "#Result\n",
+ "print \"number of days is\",D2"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 10.6, Page number 10.3"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "number of days is 30.0\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "N1=15; #number of men\n",
+ "D1=21; #number of days\n",
+ "N2=14; #number of men\n",
+ "R1=8; #number of hours\n",
+ "R2=6; #number of hours\n",
+ "\n",
+ "#Calculation\n",
+ "D2=N1*D1*R1/(N2*R2); #number of days\n",
+ "\n",
+ "#Result\n",
+ "print \"number of days is\",D2"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 10.7, Page number 10.3"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "number of days is 5.0\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "N1=100; #number of men\n",
+ "D2=40-35; #number of days\n",
+ "N2=100; #number of men joined\n",
+ "\n",
+ "#Calculation\n",
+ "D=(N1+N2)*D2/N1;\n",
+ "D1=D-D2; #number of days\n",
+ "\n",
+ "#Result\n",
+ "print \"number of days is\",D1"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 10.8, Page number 10.4"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "number of additional men is 56.0\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "N1=104; #number of men\n",
+ "D1=30; #number of days\n",
+ "D=56; #number of days\n",
+ "R1=8; #number of hours\n",
+ "R2=9; #number of hours\n",
+ "W1=2/5; #fraction of work\n",
+ "\n",
+ "#Calculation\n",
+ "D2=D-D1; #number of days\n",
+ "W2=1-W1; #rest of the work\n",
+ "N=N1*D1*R1*W2/(D2*R2*W1);\n",
+ "N2=N-N1; #number of additional men\n",
+ "\n",
+ "#Result\n",
+ "print \"number of additional men is\",N2"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 10.9, Page number 10.4"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "number of days is 25.0\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "M1=10; #number of men\n",
+ "D1=40; #number of days\n",
+ "M2=4; #number of men\n",
+ "M3=6; #number of men\n",
+ "D3=50; #number of days\n",
+ "\n",
+ "#Calculation\n",
+ "D2=((M1*D1)-(M3*D3))/M2; #number of days\n",
+ "\n",
+ "#Result\n",
+ "print \"number of days is\",D2"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 10.10, Page number 10.4"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "number of days is 30.0\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "N1=4; #number of lorries\n",
+ "D1=8; #number of days\n",
+ "R1=4; #number of tons\n",
+ "R2=3; #number of tons\n",
+ "W1=128; #number of tons\n",
+ "N2=6; #number of lorries\n",
+ "W2=540; #number of tons\n",
+ "\n",
+ "#Calculation\n",
+ "D2=N1*D1*R1*W2/(N2*R2*W1);\n",
+ "N2=N-N1; #number of days\n",
+ "\n",
+ "#Result\n",
+ "print \"number of days is\",D2"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 10.11, Page number 10.4"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "number of days is 19.0\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "N=250; #number of students\n",
+ "D=30; #number of days \n",
+ "N_1=25; #number of students added\n",
+ "D1=10; #number of days\n",
+ "\n",
+ "#Calculation\n",
+ "N1=N+N_1; #number of students\n",
+ "N2=N; #number of students\n",
+ "D2=((N*D)-(N1*D1))/N2; #number of days\n",
+ "\n",
+ "#Result\n",
+ "print \"number of days is\",D2"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 10.12, Page number 10.5"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "number of men is 1500.0\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "N1=3000; #number of men\n",
+ "D1=25-11; #number of days\n",
+ "R1=900; #rate per head\n",
+ "D2=10; #number of days\n",
+ "R2=840; #rate per head\n",
+ "\n",
+ "#Calculation\n",
+ "N=N1*D1*R1/(D2*R2); \n",
+ "N2=N-N1; #number of men\n",
+ "\n",
+ "#Result\n",
+ "print \"number of men is\",N2"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 10.13, Page number 10.5"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "required diesel is 1350.0 litres\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "N1=6; #number of diesel engines\n",
+ "D1=5; #number of hours\n",
+ "R1=1/5; \n",
+ "R2=1/8; \n",
+ "W1=900; #number of litres\n",
+ "N2=9; #number of diesel engines\n",
+ "D2=8; #number of hours\n",
+ "\n",
+ "#Calculation\n",
+ "W2=N2*D2*R2*W1/(N1*R1*D1); #required diesel(litres)\n",
+ "\n",
+ "#Result\n",
+ "print \"required diesel is\",W2,\"litres\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 10.14, Page number 10.5"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "each machine should work 16.0 h/day\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "N1=2; #number of machines\n",
+ "D1=8; #number of days\n",
+ "R1=12; #number of hours/day\n",
+ "E2=80/100; #efficiency \n",
+ "E1=90/100; #efficiency\n",
+ "W1=9000; #tonnes of coal\n",
+ "N2=3; #number of machines\n",
+ "D2=6; #number of days\n",
+ "W2=12000; #tonnes of coal\n",
+ "\n",
+ "#Calculation\n",
+ "R2=N1*D1*R1*E1*W2/(N2*D2*E2*W1); #number of hours/day\n",
+ "\n",
+ "#Result\n",
+ "print \"each machine should work\",R2,\"h/day\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 10.15, Page number 10.5"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "amount charged is 300.0 Rs\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "N1=1; #number of persons\n",
+ "D1=5/2; #number of days\n",
+ "R1=50; #amount(Rs) \n",
+ "R2=42.50; #amount(Rs) \n",
+ "W2=340; #amount(Rs)\n",
+ "N2=1; #number of persons\n",
+ "D2=10/3; #number of days\n",
+ "\n",
+ "#Calculation\n",
+ "W1=N1*D1*R1*W2/(N2*R2*D2); #amount charged(Rs)\n",
+ "\n",
+ "#Result\n",
+ "print \"amount charged is\",W1,\"Rs\""
+ ]
+ }
+ ],
+ "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
+}
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