2 June Maths Ii
This document was uploaded by user and they confirmed that they have the permission to share it. If you are author or own the copyright of this book, please report to us by using this DMCA report form. Report DMCA
Overview
Download & View 2 June Maths Ii as PDF for free.
More details
- Words: 1,614
- Pages: 32
QUANTITATIVE APTITUDE Dr. T.K. Jain. AFTERSCHOOOL M: 9414430763 [email protected] www.afterschool.tk www.afterschoool.tk
www.afterschoool.tk
120 Liters of milk and water contain milk and water in ratio of 2:1. how much water to be added to make the ratio 1:2? • Total of 2:1 = 3, so 2/3 *120 = 80 • Quantity of milk = 80, quantitiy of water = 40. milk will remain same, but its ratio will be 1:2. Thus the total quantity will be (2+1) / 1* 80 = 240 • The difference of 240 and 120 – will all be water – so quantity of water = 120.
www.afterschoool.tk
120 Liters of milk and water contain milk and water in ratio of 2:1. We remove some milk. How much milk to be taken away to make the ratio 1:2? • Total of 2:1 = 3, so 2/3 *120 = 80 • Quantity of milk = 80, quantitiy of water = 40. Water will remain same, but its ratio will be 2:1. Thus the total quantity will be (2+1) /2* 40 = 60 • The difference of 120 – 60 will all be milk withdrawn =60 ans. .
www.afterschoool.tk
Price of X and Y are in ratio of 9:5. If X costs Rs. 12000 more than Y, what is price of X & Y? • • • • •
Difference of their ratio = 9-5 =4 If the difference is 4, X has 9. If the difference is 12000, X has: 12000*9/4 = 27000. Y costs: 27000-12000=15000 Ans.
www.afterschoool.tk
If A/7 = B/11 = C/13, what is the value of (A+B+C)/C ? • For such questions, let us assume that value of A = 7, B=11 and C=13, now the condition of equality is fulfilled. • Now: (7+11+13) / 13 = 31/13 =2.38 ans.
www.afterschoool.tk
There is inverse relation between pressure and volume. If volume is increased by 20%, what will be impact on pressure?
• Let us assume that both are at 100. If volume increases by 20%, it will reach 120. Pressure has to decrease. The propensity of reduction in pressure will be in the same ratio as volume has increased – now it will be 20/120*100 = 16.67% Ans. www.afterschoool.tk
Two integer sums, whose total is 64, cannot be in ratio of: 5:6, 7:9, 3:13, 3:1? • The totals of these ratios are : 11,16,16, & 4. In any case, the total of the number should be divisible by these totals. It is not divisible by 11, therefore 5:6 cannot be such ratio.
www.afterschoool.tk
.333.. of a number is .002 of another. What is the ratio of these two numbers? • Let us assume the first number to be 3000. .333 of this will be 1000. the other number will be: 1/.002*1000 • = 500000 • Thus the ratio of the two numbers is :3:500 Ans. • Verify it: take .333.. of 3 =1, • .002*500 = 1 thus it is verified. Ans.
www.afterschoool.tk
A,B,C start a business with capital in ratio of 1/3, 1/5, ¼. A withdraws half of his capital after 6 months, but B doubles his capital after 6 months. Annual profits are Rs. 10000. How will you divide?
• Step 1: Take LCM of 3,5, and 4. =60.multiply it to all the ratios, new ratios are: 20:12:15. Ratio for last 6 month is: 10:24:15 • The combined ratio is : 15:18:15. dividing each by 3, =5:6:5 or 5/16,6/16, & 5/16 • A,B,C will get: 3125,3750,3125 ans.
www.afterschoool.tk
A,B,C start a business with capital in ratio of 1/2, 1/3, ¼. A withdraws half of his capital after 2 months, but B doubles his capital after 8 months. Annual profits are Rs. 10000. How will you divide?
• LCM of 2,3,4 = 12, multiplying it to 3 ratios, new ratio = 6:4:3 • A = 6*2 +3*10 = 42 • B=4*8 + 8*4 =64 • C = 3*12 =36 • Ratio = 42:64:36 = 21:32:18. Total =71; A =21/71*10000 =2958, B = 32/71*10000=4507 remaining to C=2535 www.afterschoool.tk
If 6(A)=8(B)=9(C) , A,B,C represent capitals of A,B,C. what is the ratio of their capital? • Take LCM of 6,8,9 = 72. • Let us assume 6(A)=8(B)=9(C) =72 • 6A = 72, A = 12. 8 B = 72, B =9; 9C= 72, C= 8. • Ratio of their capitals is : 12:9:8 Ans.
www.afterschoool.tk
A & B make investments in ratio of 12:11. A invested money for 11 months and took 80% profit. For how much time did B invest money?
• Profit sharing ratio = capital*time • A’s ratio = 12*11 = 132. • This is 80%, then share of B = 132*20/80 = 33 • B invested the money for 33/11 = 3 months. Ans.
www.afterschoool.tk
X +1/X =3, what will be the value of X^2 +1/X^2? • • • • • •
Make square of (X +1/X =3) We get: X^2 +2*X*1/X + 1/X^2 = 9 (x *1/X = 1) = X^2 +2 + 1/X^2 = 9 =X^2 + 1/X^2 = 9-2 =7 ANS. www.afterschoool.tk
[2.3^3- .027]/ (2.3^2+.69+.09) =? • • • • • • •
This is a question of the format: A^3 – B^3 / (A^2+AB+B^2) = A-B Therefore answer is A-B A = 2.3, B = .3 =2.3-.3 = 2 ans. Note the formula: A^3 – B^3 = (a-b)(a^2+ab+b^2) A^3 + B^3 = (a+b)(a^2-ab+b^2) www.afterschoool.tk
A+b+c = 9, (a^3+b^3+c^33abc) = 108. What is value fo ab+bc+ac ? • Formulae is: • (a^3+b^3+c^3-3abc)=(a+b+c) [(a+b+c)^2 – 3(ab+bc+ac)] • Therefore : 108=9*[81-3X] • 108=729-27x • X=621/27 = 23 Ans.
www.afterschoool.tk
What is the value of (x+y+z)^2, if x^2+y^2+z^2 = 14, and (xy+zx+yz) = 11. • (x+y+z)^2, =[ x^2+y^2+z^2 + 2(xy+zx+yz) ] • =14+22 = 36 Ans.
www.afterschoool.tk
What is the value of (14+7)^4? • =(20+1)^4 • (a+b)^4 = • A^4+ 4a^3b+6a^2b^2+4a ^1b^3+b • =160000+32000+2 400+80+1 • =194481 Ans.
121 1331 14641 1 5 10 10 5 1 1 6 15 20 15 6 1 1 7 21 35 35 21 7 1
www.afterschoool.tk
Out of three numbers, first is twice the second and three times the third. Average of these 3 numbers is 88, what is the difference of I & III number? • Let us assume the III no. to be X, Ist no. is 3X, II is 3/2X • Average of these is (X+3X+1.5X) /3 = 88 • 11/2X = 88*3; X = 88*3*2/11 • X = 48 • Difference of I & III = 3X-X = 2X = 2*48 = 96 ans. www.afterschoool.tk
What is right angle? • 90 degree
www.afterschoool.tk
What is acute angle? • Less then 90 degree.
www.afterschoool.tk
What is reflex angle? • More than 180 but less than 360 degree.
www.afterschoool.tk
What is obtuse angle? • More than 90 degrees.
www.afterschoool.tk
What is the diffference between line, ray and line segment?
• Line has no end points (infinite on both the ends) • Ray = one end point and infinite on one side. • Line segment = two end points.
www.afterschoool.tk
Sum of all interior angles of a regular polygon? • • • • • •
=(2n-4) 90 degree For example for a triangle: = (2*3 -4) *90 degree =2*90 = 180 For a septagon: (2*7 – 4)*90 = 900 degrees. www.afterschoool.tk
Thanks Afterschoool conducts three year integrated PGPSE (after class 12 along with IAS, CA & CS) and 18 month PGPSE (Post Graduate Programme in Social Entrepreneurship) along with preparation for CS / CFP / CFA /CMA / FRM. This course is also available online also. It also conducts workshops on social entrepreneurship in schools and colleges all over India – start social entrepreneurship club in your institution today with the help from afterschoool and help us in developing society.
www.afterschoool.tk
About AFTERSCHOOOL PGPSE – the best programme for developing great entrepreneurs • Most flexible, adaptive but rigorous programme • Available in distance learning mode • Case study focused- latest cases • Industry oriented practical curriculum • Designed to make you entrepreneurs – not just an employee • Option to take up part time job – so earn while you learn www.afterschoool.tk
Workshops from AFTERSCHOOOL • • • • • • • • •
IIF, Delhi CIPS, Jaipur ICSI Hyderabad Branch Gyan Vihar, Jaipur Apex Institute of Management, Jaipur Aravali Institute of Management, Jodhpur Xavier Institute of Management, Bhubaneshwar Pacific Institute, Udaipur Engineering College, Hyderabad
www.afterschoool.tk
Specialisations: • • • • • • • • •
Spiritualising business and society Rural development and transformation HRD and Education, Social Development NGO and voluntary work Investment analysis,microfinance and inclusion Retail sector Hospital management and Health care Hospitality sector and culture and heritage Other sectors of high growth, high technology and social relevance
www.afterschoool.tk
Salient features: • The only programme of its kind (in the whole world) • No publicity and low profile course • For those who wants to achieve success in life – not just a degree • Indepth knowledge and expertise • Professional approach • Strong intellectual and business capabilities • World class approach • Scholarships for those from poor economic background • Latest and constantly changing curriculum – keeping pace with the time
www.afterschoool.tk
Components Meditation, spiritualisation, and self development Business plan Essential softwares for business Research projects Participation in conferences / seminars Workshops on leadership, team building etc. Written submissions of research projects/articles / papers Interview of entrepreneurs, writing biographies of entrepreneurs • Editing of journals / newsletters • Consultancy / research projects • Assignments, communication skill workshops • • • • • • • •
www.afterschoool.tk
Pedagogy
• Case analysis • Quiz, seminars, workshops, games, • Visits to entrepreneurs and industrial visits • Presentations • Group discussions and group projects • Periodic self assessment • Mentoring and counselling
www.afterschoool.tk
www.afterschoool.tk social entrepreneurship for better society
www.afterschoool.tk
www.afterschoool.tk
120 Liters of milk and water contain milk and water in ratio of 2:1. how much water to be added to make the ratio 1:2? • Total of 2:1 = 3, so 2/3 *120 = 80 • Quantity of milk = 80, quantitiy of water = 40. milk will remain same, but its ratio will be 1:2. Thus the total quantity will be (2+1) / 1* 80 = 240 • The difference of 240 and 120 – will all be water – so quantity of water = 120.
www.afterschoool.tk
120 Liters of milk and water contain milk and water in ratio of 2:1. We remove some milk. How much milk to be taken away to make the ratio 1:2? • Total of 2:1 = 3, so 2/3 *120 = 80 • Quantity of milk = 80, quantitiy of water = 40. Water will remain same, but its ratio will be 2:1. Thus the total quantity will be (2+1) /2* 40 = 60 • The difference of 120 – 60 will all be milk withdrawn =60 ans. .
www.afterschoool.tk
Price of X and Y are in ratio of 9:5. If X costs Rs. 12000 more than Y, what is price of X & Y? • • • • •
Difference of their ratio = 9-5 =4 If the difference is 4, X has 9. If the difference is 12000, X has: 12000*9/4 = 27000. Y costs: 27000-12000=15000 Ans.
www.afterschoool.tk
If A/7 = B/11 = C/13, what is the value of (A+B+C)/C ? • For such questions, let us assume that value of A = 7, B=11 and C=13, now the condition of equality is fulfilled. • Now: (7+11+13) / 13 = 31/13 =2.38 ans.
www.afterschoool.tk
There is inverse relation between pressure and volume. If volume is increased by 20%, what will be impact on pressure?
• Let us assume that both are at 100. If volume increases by 20%, it will reach 120. Pressure has to decrease. The propensity of reduction in pressure will be in the same ratio as volume has increased – now it will be 20/120*100 = 16.67% Ans. www.afterschoool.tk
Two integer sums, whose total is 64, cannot be in ratio of: 5:6, 7:9, 3:13, 3:1? • The totals of these ratios are : 11,16,16, & 4. In any case, the total of the number should be divisible by these totals. It is not divisible by 11, therefore 5:6 cannot be such ratio.
www.afterschoool.tk
.333.. of a number is .002 of another. What is the ratio of these two numbers? • Let us assume the first number to be 3000. .333 of this will be 1000. the other number will be: 1/.002*1000 • = 500000 • Thus the ratio of the two numbers is :3:500 Ans. • Verify it: take .333.. of 3 =1, • .002*500 = 1 thus it is verified. Ans.
www.afterschoool.tk
A,B,C start a business with capital in ratio of 1/3, 1/5, ¼. A withdraws half of his capital after 6 months, but B doubles his capital after 6 months. Annual profits are Rs. 10000. How will you divide?
• Step 1: Take LCM of 3,5, and 4. =60.multiply it to all the ratios, new ratios are: 20:12:15. Ratio for last 6 month is: 10:24:15 • The combined ratio is : 15:18:15. dividing each by 3, =5:6:5 or 5/16,6/16, & 5/16 • A,B,C will get: 3125,3750,3125 ans.
www.afterschoool.tk
A,B,C start a business with capital in ratio of 1/2, 1/3, ¼. A withdraws half of his capital after 2 months, but B doubles his capital after 8 months. Annual profits are Rs. 10000. How will you divide?
• LCM of 2,3,4 = 12, multiplying it to 3 ratios, new ratio = 6:4:3 • A = 6*2 +3*10 = 42 • B=4*8 + 8*4 =64 • C = 3*12 =36 • Ratio = 42:64:36 = 21:32:18. Total =71; A =21/71*10000 =2958, B = 32/71*10000=4507 remaining to C=2535 www.afterschoool.tk
If 6(A)=8(B)=9(C) , A,B,C represent capitals of A,B,C. what is the ratio of their capital? • Take LCM of 6,8,9 = 72. • Let us assume 6(A)=8(B)=9(C) =72 • 6A = 72, A = 12. 8 B = 72, B =9; 9C= 72, C= 8. • Ratio of their capitals is : 12:9:8 Ans.
www.afterschoool.tk
A & B make investments in ratio of 12:11. A invested money for 11 months and took 80% profit. For how much time did B invest money?
• Profit sharing ratio = capital*time • A’s ratio = 12*11 = 132. • This is 80%, then share of B = 132*20/80 = 33 • B invested the money for 33/11 = 3 months. Ans.
www.afterschoool.tk
X +1/X =3, what will be the value of X^2 +1/X^2? • • • • • •
Make square of (X +1/X =3) We get: X^2 +2*X*1/X + 1/X^2 = 9 (x *1/X = 1) = X^2 +2 + 1/X^2 = 9 =X^2 + 1/X^2 = 9-2 =7 ANS. www.afterschoool.tk
[2.3^3- .027]/ (2.3^2+.69+.09) =? • • • • • • •
This is a question of the format: A^3 – B^3 / (A^2+AB+B^2) = A-B Therefore answer is A-B A = 2.3, B = .3 =2.3-.3 = 2 ans. Note the formula: A^3 – B^3 = (a-b)(a^2+ab+b^2) A^3 + B^3 = (a+b)(a^2-ab+b^2) www.afterschoool.tk
A+b+c = 9, (a^3+b^3+c^33abc) = 108. What is value fo ab+bc+ac ? • Formulae is: • (a^3+b^3+c^3-3abc)=(a+b+c) [(a+b+c)^2 – 3(ab+bc+ac)] • Therefore : 108=9*[81-3X] • 108=729-27x • X=621/27 = 23 Ans.
www.afterschoool.tk
What is the value of (x+y+z)^2, if x^2+y^2+z^2 = 14, and (xy+zx+yz) = 11. • (x+y+z)^2, =[ x^2+y^2+z^2 + 2(xy+zx+yz) ] • =14+22 = 36 Ans.
www.afterschoool.tk
What is the value of (14+7)^4? • =(20+1)^4 • (a+b)^4 = • A^4+ 4a^3b+6a^2b^2+4a ^1b^3+b • =160000+32000+2 400+80+1 • =194481 Ans.
121 1331 14641 1 5 10 10 5 1 1 6 15 20 15 6 1 1 7 21 35 35 21 7 1
www.afterschoool.tk
Out of three numbers, first is twice the second and three times the third. Average of these 3 numbers is 88, what is the difference of I & III number? • Let us assume the III no. to be X, Ist no. is 3X, II is 3/2X • Average of these is (X+3X+1.5X) /3 = 88 • 11/2X = 88*3; X = 88*3*2/11 • X = 48 • Difference of I & III = 3X-X = 2X = 2*48 = 96 ans. www.afterschoool.tk
What is right angle? • 90 degree
www.afterschoool.tk
What is acute angle? • Less then 90 degree.
www.afterschoool.tk
What is reflex angle? • More than 180 but less than 360 degree.
www.afterschoool.tk
What is obtuse angle? • More than 90 degrees.
www.afterschoool.tk
What is the diffference between line, ray and line segment?
• Line has no end points (infinite on both the ends) • Ray = one end point and infinite on one side. • Line segment = two end points.
www.afterschoool.tk
Sum of all interior angles of a regular polygon? • • • • • •
=(2n-4) 90 degree For example for a triangle: = (2*3 -4) *90 degree =2*90 = 180 For a septagon: (2*7 – 4)*90 = 900 degrees. www.afterschoool.tk
Thanks Afterschoool conducts three year integrated PGPSE (after class 12 along with IAS, CA & CS) and 18 month PGPSE (Post Graduate Programme in Social Entrepreneurship) along with preparation for CS / CFP / CFA /CMA / FRM. This course is also available online also. It also conducts workshops on social entrepreneurship in schools and colleges all over India – start social entrepreneurship club in your institution today with the help from afterschoool and help us in developing society.
www.afterschoool.tk
About AFTERSCHOOOL PGPSE – the best programme for developing great entrepreneurs • Most flexible, adaptive but rigorous programme • Available in distance learning mode • Case study focused- latest cases • Industry oriented practical curriculum • Designed to make you entrepreneurs – not just an employee • Option to take up part time job – so earn while you learn www.afterschoool.tk
Workshops from AFTERSCHOOOL • • • • • • • • •
IIF, Delhi CIPS, Jaipur ICSI Hyderabad Branch Gyan Vihar, Jaipur Apex Institute of Management, Jaipur Aravali Institute of Management, Jodhpur Xavier Institute of Management, Bhubaneshwar Pacific Institute, Udaipur Engineering College, Hyderabad
www.afterschoool.tk
Specialisations: • • • • • • • • •
Spiritualising business and society Rural development and transformation HRD and Education, Social Development NGO and voluntary work Investment analysis,microfinance and inclusion Retail sector Hospital management and Health care Hospitality sector and culture and heritage Other sectors of high growth, high technology and social relevance
www.afterschoool.tk
Salient features: • The only programme of its kind (in the whole world) • No publicity and low profile course • For those who wants to achieve success in life – not just a degree • Indepth knowledge and expertise • Professional approach • Strong intellectual and business capabilities • World class approach • Scholarships for those from poor economic background • Latest and constantly changing curriculum – keeping pace with the time
www.afterschoool.tk
Components Meditation, spiritualisation, and self development Business plan Essential softwares for business Research projects Participation in conferences / seminars Workshops on leadership, team building etc. Written submissions of research projects/articles / papers Interview of entrepreneurs, writing biographies of entrepreneurs • Editing of journals / newsletters • Consultancy / research projects • Assignments, communication skill workshops • • • • • • • •
www.afterschoool.tk
Pedagogy
• Case analysis • Quiz, seminars, workshops, games, • Visits to entrepreneurs and industrial visits • Presentations • Group discussions and group projects • Periodic self assessment • Mentoring and counselling
www.afterschoool.tk
www.afterschoool.tk social entrepreneurship for better society
www.afterschoool.tk
Related Documents
2 June Maths Ii
November 2019 25
2 June Maths Ii
November 2019 12
10 June Maths Ii
November 2019 23
30 June Maths Ii
June 2020 23
17 June Maths Ii
November 2019 21