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diff --git a/Quantitative_Aptitude_for_Competitive_Examinations/Chapter20.ipynb b/Quantitative_Aptitude_for_Competitive_Examinations/Chapter20.ipynb new file mode 100755 index 00000000..aa2212ac --- /dev/null +++ b/Quantitative_Aptitude_for_Competitive_Examinations/Chapter20.ipynb @@ -0,0 +1,534 @@ +{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#20: Trains"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 20.1, Page number 20.4"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "time taken to cross a telegraph post is 6.6 s\n",
+ "time taken to cross a man running in same direction is 7.33 s\n",
+ "time taken to cross a man running in opposite direction is 6.0 s\n",
+ "time taken to cross a platform is 21.0 s\n",
+ "time taken to cross a train is 16.8 s\n",
+ "time taken to cross another train is 2 minutes 48.0 s\n",
+ "time taken to cross another train is 7.2 s\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "s=60; #speed(km/h)\n",
+ "Lt=110; #length of train(m)\n",
+ "L1=0; \n",
+ "L2=240; #length of pplatform(m)\n",
+ "L3=170; #length of train(m)\n",
+ "v1=6; #speed of man(km/h)\n",
+ "v2=54; #speed of another train(km/hr)\n",
+ "v3=80; #speed of another train(km/hr)\n",
+ "\n",
+ "#Calculation\n",
+ "Vt=s*5/18; #speed of train(m/s)\n",
+ "V1=v1*5/18; #speed of man(m/s)\n",
+ "V2=v2*5/18; #speed of another train(m/s)\n",
+ "V3=v3*5/18; #speed of another train(m/s)\n",
+ "t1=(Lt+L1)/Vt; #time taken to cross a telegraph post(s)\n",
+ "t2=(Lt+L1)/(Vt-V1); #time taken to cross a man running in same direction(s)\n",
+ "t3=(Lt+L1)/(Vt+V1); #time taken to cross a man running in opposite direction(s) \n",
+ "t4=(Lt+L2)/Vt; #time taken to cross a platform(s)\n",
+ "t5=(Lt+L3)/Vt; #time taken to cross a train(s)\n",
+ "t6=(Lt+L3)/(Vt-V2); #time taken to cross another train(s)\n",
+ "t6m=int(t6/60); #time(m)\n",
+ "t6s=t6-(t6m*60);\n",
+ "t7=(Lt+L3)/(Vt+V3); #time taken to cross another train(s)\n",
+ "\n",
+ "#Result\n",
+ "print \"time taken to cross a telegraph post is\",t1,\"s\"\n",
+ "print \"time taken to cross a man running in same direction is\",round(t2,2),\"s\"\n",
+ "print \"time taken to cross a man running in opposite direction is\",t3,\"s\"\n",
+ "print \"time taken to cross a platform is\",t4,\"s\"\n",
+ "print \"time taken to cross a train is\",t5,\"s\"\n",
+ "print \"time taken to cross another train is\",t6m,\"minutes\",t6s,\"s\"\n",
+ "print \"time taken to cross another train is\",t7,\"s\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 20.2, Page number 20.5"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "length of platform is 240.0 m\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "s=54; #speed of train(km/hr)\n",
+ "t1=36; #time(s)\n",
+ "t2=20; #time(s)\n",
+ "V1=0;\n",
+ "V2=0;\n",
+ "L2=0;\n",
+ "\n",
+ "#Calculation\n",
+ "Vt=s*5/18; #speed of train(m/s)\n",
+ "a=Vt*(t1-t2);\n",
+ "L1=a+L2-(V1*t1)-(V2*t2); #length of platform(m)\n",
+ "\n",
+ "#Result\n",
+ "print \"length of platform is\",L1,\"m\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 20.3, Page number 20.6"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "speed of train is 12.5 m/s\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "L1=0; #length of man(m)\n",
+ "L2=150; #length of platform(m)\n",
+ "t1=10; #time(s)\n",
+ "t2=22; #time(s)\n",
+ "V1=0;\n",
+ "V2=0;\n",
+ "\n",
+ "#Calculation\n",
+ "a=(L1+(V1*t1))-(L2+(V2*t2));\n",
+ "Vt=a/(t1-t2); #speed of train(m/s)\n",
+ "\n",
+ "#Result\n",
+ "print \"speed of train is\",Vt,\"m/s\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 20.4, Page number 20.6"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "length of train is 50.0 m\n",
+ "length of platform is 75.0 m\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "L2=0; #length of man(m)\n",
+ "t1=18; #time(s)\n",
+ "t2=10; #time(s)\n",
+ "V1=0;\n",
+ "V2=7*5/18; #speed(m/s)\n",
+ "Vt=25*5/18; #speed of train(m/s)\n",
+ "\n",
+ "#Calculation\n",
+ "Lt=((Vt-V2)*t2)-L2; #length of train(m)\n",
+ "L1=((Vt-V1)*t1)-Lt; #length of platform(m)\n",
+ "\n",
+ "#Result\n",
+ "print \"length of train is\",Lt,\"m\"\n",
+ "print \"length of platform is\",L1,\"m\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 20.5, Page number 20.7"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "length of train is 45.0 m\n",
+ "length of platform is 75.0 m\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "L2=0; #length of man(m)\n",
+ "t1=12; #time(s)\n",
+ "t2=6; #time(s)\n",
+ "V1=0;\n",
+ "V2=-9*5/18; #speed(m/s)\n",
+ "Vt=36*5/18; #speed of train(m/s)\n",
+ "\n",
+ "#Calculation\n",
+ "Lt=((Vt-V1)*t1)-L1; #length of train(m)\n",
+ "L1=((Vt-V1)*t1)-Lt; #length of platform(m)\n",
+ "\n",
+ "#Result\n",
+ "print \"length of train is\",Lt,\"m\"\n",
+ "print \"length of platform is\",L1,\"m\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 20.6, Page number 20.7"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "speed of train is 11.0 m/s\n",
+ "length of train is 65.0 m\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "L1=210; #length of tunnel(m) \n",
+ "L2=122; #length of tunnel(m)\n",
+ "t1=25; #time(s)\n",
+ "t2=17; #time(s)\n",
+ "V1=0;\n",
+ "V2=0; #speed(m/s)\n",
+ "\n",
+ "#Calculation\n",
+ "a=(L1+(V1*t1))-(L2+(V2*t2));\n",
+ "Vt=a/(t1-t2); #speed of train(m/s)\n",
+ "Lt=((Vt-V1)*t1)-L1; #length of train(m)\n",
+ "\n",
+ "#Result\n",
+ "print \"speed of train is\",Vt,\"m/s\"\n",
+ "print \"length of train is\",Lt,\"m\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 20.7, Page number 20.7"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 17,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "time taken by the train to cross the platform is 21.0 s\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "L1=250; #length of bridge(m) \n",
+ "L2=130; #length of platform(m)\n",
+ "Lt=150; #length of train(m)\n",
+ "t1=30; #time(s)\n",
+ "V1=0;\n",
+ "V2=0; #speed(m/s)\n",
+ "\n",
+ "#Calculation\n",
+ "t2=(Lt+L2)*t1/(Lt+L1); #time taken by the train to cross the platform(s)\n",
+ "\n",
+ "#Result\n",
+ "print \"time taken by the train to cross the platform is\",t2,\"s\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 20.8, Page number 20.8"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 19,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "time taken by the second train is 64.0 s\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "Lt1_Lt2=100; #difference in length(m)\n",
+ "Vt1=90*5/18; #speed of 1st train(m/s)\n",
+ "Vt2=45*5/18; #speed of 2nd train(m/s)\n",
+ "t1=36; #time(s)\n",
+ "\n",
+ "#Calculation\n",
+ "t2=((Vt1*t1)-Lt1_Lt2)/Vt2; #time taken by the second train(s)\n",
+ "\n",
+ "#Result\n",
+ "print \"time taken by the second train is\",t2,\"s\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 20.9, Page number 20.8"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "speed of train is 94.0 km/h\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "Lt=100; #length of train(m)\n",
+ "V=-6; #speed of train(m/s)\n",
+ "t=18/5; #time(s)\n",
+ "L=0;\n",
+ "\n",
+ "#Calculation\n",
+ "x=t*1/t;\n",
+ "Vt=(Lt+L+(x*V))/x; #speed of train(m/s)\n",
+ "\n",
+ "#Result\n",
+ "print \"speed of train is\",Vt,\"km/h\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "collapsed": true
+ },
+ "source": [
+ "##Example number 20.10, Page number 20.8"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "speed of second person is 3.0 km/h\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "Lt=75; #length of train(m)\n",
+ "L1=L2=0;\n",
+ "t1=18; #time(s)\n",
+ "t2=15; #time(s)\n",
+ "V1=6*5/18; #speed(km/h)\n",
+ "\n",
+ "#Calculation\n",
+ "a=(Lt+L1)/t1;\n",
+ "b=(Lt+L2)/t2;\n",
+ "V2=(a+V1-b)*18/5; #speed of second person(km/h)\n",
+ "\n",
+ "#Result\n",
+ "print \"speed of second person is\",V2,\"km/h\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 20.11, Page number 20.9"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "speed of faster train is 42.0 m/s\n",
+ "speed of slower train is 38.0 m/s\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "L1=130; #length of train(m)\n",
+ "L2=110; #length of train(m)\n",
+ "t1=3;\n",
+ "t2=60; #time(s)\n",
+ "\n",
+ "#Calculation\n",
+ "s1=((L1+L2)/2)*((1/t1)+(1/t2)); #speed of faster train(m/s)\n",
+ "s2=((L1+L2)/2)*((1/t1)-(1/t2)); #speed of slower train(m/s)\n",
+ "\n",
+ "#Result\n",
+ "print \"speed of faster train is\",s1,\"m/s\"\n",
+ "print \"speed of slower train is\",s2,\"m/s\""
+ ]
+ }
+ ],
+ "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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