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diff --git a/Quantitative_Aptitude_for_Competitive_Examinations/Chapter6.ipynb b/Quantitative_Aptitude_for_Competitive_Examinations/Chapter6.ipynb new file mode 100755 index 00000000..7d2fb138 --- /dev/null +++ b/Quantitative_Aptitude_for_Competitive_Examinations/Chapter6.ipynb @@ -0,0 +1,743 @@ +{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#6: Average"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 6.1 Page number 6.5"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "average age of students in both sections is 10.86 years\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "m=40; #number of students in A\n",
+ "a=10; #average age in A\n",
+ "b=12; #average age in B\n",
+ "n=30; #number of students in B\n",
+ "\n",
+ "#Calculation\n",
+ "average=((m*a)+(n*b))/(m+n); #average age of students in both sections\n",
+ "\n",
+ "#Result\n",
+ "print \"average age of students in both sections is\",round(average,2),\"years\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 6.2 Page number 6.5"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "average of 2 numbers is 9.0\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "m=5; #number of quantities\n",
+ "n=3; #number of quantities\n",
+ "a=6; #average of 5 quantities\n",
+ "b=4; #average of 3 quantities\n",
+ "\n",
+ "#Calculation\n",
+ "average=((m*a)-(n*b))/(m-n); #average of 2 numbers\n",
+ "\n",
+ "#Result\n",
+ "print \"average of 2 numbers is\",average"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 6.3 Page number 6.5"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "average price of pen is 12.0 Rs\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "m=30; #number of pens\n",
+ "n=75; #number of pencils\n",
+ "p=2; #average price of pencil\n",
+ "S=510; #cost of pens and pencils\n",
+ "\n",
+ "#Calculation\n",
+ "y=(S-(n*p))/m; #average price of pen(Rs)\n",
+ "\n",
+ "#Result\n",
+ "print \"average price of pen is\",y,\"Rs\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 6.4 Page number 6.5"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "age of A is 22.0 years\n",
+ "age of B is 18.0 years\n",
+ "age of C is 20.0 years\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "aplusb=2*20; #average age of A and B\n",
+ "bplusc=2*19; #average age of B and C\n",
+ "cplusa=2*21; #average age of C and A\n",
+ "\n",
+ "#Calculation\n",
+ "aplusbplusc=(aplusb+bplusc+cplusa)/2;\n",
+ "a=aplusbplusc-bplusc; #age of A(years)\n",
+ "b=aplusbplusc-cplusa; #age of B(years)\n",
+ "c=aplusbplusc-aplusb; #age of C(years)\n",
+ "\n",
+ "#Result\n",
+ "print \"age of A is\",a,\"years\"\n",
+ "print \"age of B is\",b,\"years\"\n",
+ "print \"age of C is\",c,\"years\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 6.5 Page number 6.6"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "average monthly income is 2805.0 Rs\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "e1=2200; #average monthly expenditure for 3 months(Rs)\n",
+ "n1=3; #number of months in 1st case\n",
+ "e2=2550; #average monthly expenditure for 4 months(Rs)\n",
+ "n2=4; #number of months in 2nd case\n",
+ "e3=3120; #average monthly expenditure for 5 months(Rs)\n",
+ "n3=5; #number of months in 3rd case\n",
+ "s=1260; #total saving(Rs)\n",
+ "\n",
+ "#Calculation\n",
+ "I=(e1*n1)+(e2*n2)+(e3*n3)+s; #total yearly income(Rs)\n",
+ "average=I/12; #average monthly income(Rs)\n",
+ "\n",
+ "#Result\n",
+ "print \"average monthly income is\",average,\"Rs\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 6.6 Page number 6.6"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "temperature of tuesday is 36 C\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "TWT=37; #average temperature on tuesday, wednesday, thursday(C)\n",
+ "FWT=38; #average temperature on wednesday, thursday, friday(C)\n",
+ "R=39; #temperature on friday(C)\n",
+ "n=3; #number of quantities\n",
+ "\n",
+ "#Calculation\n",
+ "T=R-((FWT-TWT)*n); #temperature of tuesday(C)\n",
+ "\n",
+ "#Result\n",
+ "print \"temperature of tuesday is\",T,\"C\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 6.7 Page number 6.6"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "temperature of september is 26 C\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "n=3; #number of quantities\n",
+ "J=29; #temperature of june(C)\n",
+ "JJA=31; #average temperature of june, july august(C)\n",
+ "JAS=30; #average temperature of july, august, september(C)\n",
+ "\n",
+ "#Calculation\n",
+ "S=J+((JAS-JJA)*n); #temperature of september(C)\n",
+ "\n",
+ "#Result\n",
+ "print \"temperature of september is\",S,\"C\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 6.8 Page number 6.6"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "weight of teacher is 63.0 kg\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "n1=29; #number of students in class\n",
+ "n2=30; #number when teacher is included\n",
+ "w1=48; #average weight of 29 students(kg)\n",
+ "w=0.5; #change in average weight of 30 members(kg)\n",
+ "\n",
+ "#Calculation\n",
+ "wt=((n2-n1)*w1)+(w*n2); #weight of teacher(kg)\n",
+ "\n",
+ "#Result\n",
+ "print \"weight of teacher is\",wt,\"kg\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 6.9 Page number 6.7"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "weight of boy who left the class is 49.9 kg\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "n1=50; #number of boys in class\n",
+ "w1=45; #original average(kg)\n",
+ "n2=49; #number of boys when one leaves the class\n",
+ "dw=0.1; #reduction in average weight(kg)\n",
+ "\n",
+ "#Calculation\n",
+ "a=(n1-n2)*w1;\n",
+ "b=-dw*n2;\n",
+ "w=a-b; #weight of boy who left the class(kg)\n",
+ "\n",
+ "#Result\n",
+ "print \"weight of boy who left the class is\",w,\"kg\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 6.10 Page number 6.7"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "average age of 10 new students is 16.0 years\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "n1=40; #number of students\n",
+ "na=10; #number of students newly admitted\n",
+ "a1=15; #original average(years)\n",
+ "a=0.2; #change in average(year)\n",
+ "\n",
+ "#Calculation\n",
+ "sa=(na*a1)+(a*(n1+na)); #sum of weight(kg)\n",
+ "avga=sa/na; #average age of 10 new students(years)\n",
+ "\n",
+ "#Result\n",
+ "print \"average age of 10 new students is\",avga,\"years\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 6.11 Page number 6.7"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "average weight of 20 students is 55.0 kg\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "n1=30; #number of students\n",
+ "n=20; #number of students newly admitted\n",
+ "a1=60; #original average(kg)\n",
+ "a=-2; #change in average weight(kg)\n",
+ "\n",
+ "#Calculation\n",
+ "s=(n*a1)+(a*(n1+n)); #sum of weight(kg)\n",
+ "aw=s/n; #average weight of 20 students(kg)\n",
+ "\n",
+ "#Result\n",
+ "print \"average weight of 20 students is\",aw,\"kg\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 6.12 Page number 6.7"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "value of 6th result is 56\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "n1=6; #number of results\n",
+ "a1=49; #average of 1st six results\n",
+ "a2=52; #average of last six results\n",
+ "n2=11; \n",
+ "a3=50; #average of 11 results\n",
+ "\n",
+ "#Calculation\n",
+ "v6=(n1*a1)+(n1*a2)-(n2*a3); #value of 6th result\n",
+ "\n",
+ "#Result\n",
+ "print \"value of 6th result is\",v6"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 6.13 Page number 6.8"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 18,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "average after 21 innings is 67.0 runs\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "n1=20; #number of innings\n",
+ "n2=21; #number of innings in 2nd case\n",
+ "r2=107; #number of runs\n",
+ "a2=2; #change in average(runs)\n",
+ "\n",
+ "#Calculation\n",
+ "a1=a2*n2;\n",
+ "A=(r2-a1)/(n2-n1); \n",
+ "A=A+2; #average after 21 innings(runs)\n",
+ "\n",
+ "#Result\n",
+ "print \"average after 21 innings is\",A,\"runs\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 6.14 Page number 6.8"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 19,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "final average is 28.0 runs\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "Sa=6; #number of runs in last 2 innings(runs)\n",
+ "na=2; #number of innings\n",
+ "deltaA=-2; #drop in average runs\n",
+ "A1=750; #number of runs\n",
+ "\n",
+ "#Calculation\n",
+ "#from the equation 6=(2*750/N)-(2*N+4) we get a quadratic equation in N \n",
+ "a=-deltaA; #coefficient of N**2\n",
+ "b=Sa-(na*deltaA); #coefficient of N\n",
+ "c=-na*A1; #constant term\n",
+ "N=((-b)+math.sqrt((b**2)-(4*a*c)))/(2*a); #number of innings\n",
+ "A=A1/N; #original average\n",
+ "FA=A-na; #final average(runs)\n",
+ "\n",
+ "#Result\n",
+ "print \"final average is\",FA,\"runs\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 6.15 Page number 6.8"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 24,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "new average of bowler is 9.0 or 9.33333333333\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "sa=52; #number of runs\n",
+ "na=3; #number of wickets\n",
+ "A1=200; #average of bowler\n",
+ "deltaA=1; #change in average\n",
+ "\n",
+ "#Calculation\n",
+ "#from the equation 52=(3*200/N)+(+1)*(N+3) we get a quadratic equation in N \n",
+ "a=deltaA; #coefficient of N**2\n",
+ "b=na-sa; #coefficient of N\n",
+ "c=na*A1; #constant term\n",
+ "N1=((-b)+math.sqrt((b**2)-(4*a*c)))/(2*a); #number of innings\n",
+ "N2=((-b)-math.sqrt((b**2)-(4*a*c)))/(2*a); #number of innings\n",
+ "NA1=(A1+sa)/(N1+na); #new average\n",
+ "NA2=(A1+sa)/(N2+na); #new average\n",
+ "x=NA2-int(NA2);\n",
+ "\n",
+ "#Result\n",
+ "print \"new average of bowler is\",NA1,\"or\",NA2"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 6.16 Page number 6.9"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 25,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "weight of new student is 62.5 kg\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "n=15; #number of students\n",
+ "da=1.5; #change in average\n",
+ "wr=40; #weight of removed student(kg)\n",
+ "\n",
+ "#Calculation\n",
+ "wn=wr+(n*da); #weight of new student(kg)\n",
+ "\n",
+ "#Result\n",
+ "print \"weight of new student is\",wn,\"kg\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 6.17 Page number 6.9"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 26,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "average age of 2 players is 15.5 years\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "n=11; #number of players\n",
+ "ac=25; #age of captain(years)\n",
+ "awk=28; #age of wicket keeper(years)\n",
+ "da=-2; #change in average(years)\n",
+ "\n",
+ "#Calculation\n",
+ "S=(ac+awk)+(n*da); #sum of age of replacing players(years)\n",
+ "A=S/2; #average age of 2 players(years)\n",
+ "\n",
+ "#Result\n",
+ "print \"average age of 2 players is\",A,\"years\""
+ ]
+ }
+ ],
+ "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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