2 June Maths Iii
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QUANTITATIVE APTITUDE Dr. T.K. Jain. AFTERSCHOOOL M: 9414430763 [email protected] www.afterschool.tk www.afterschoool.tk
www.afterschoool.tk
If A,B,C denote areas of three faces of a cuboid (rectangular faces). What is the volume? • • • • •
Volume = L*B*H L= length, B= bredth, H = height Faces are : L*B, L*H, B*H. Multiplying them together, we have: L^2* B^2*H^2. So the Volume is square root of ABC. Ans.
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A & B run a 1000 m. race. A gives B a start of 50 meters and still beat him by 1 minute. If A runs @ 8 KM per hour, find B’s speed?
• A’s speed = 8000 m per 60 minutes. • Time take by A = 60*1000/8000 = 7.5 minutes • B ran 950 meters in 8.5 minutes. • Speed of B = 950*60/8.5 = 6706 meters per hours or 6.7 km. per hour (approx. ) ans. www.afterschoool.tk
The average of first 5 numbers is three times the 6th number. If the average of all the 6 numbers is 10.667, find the 6th number? • • • • • • •
Let us assume the average to be x Total of 5 numbers is 5x. 6th number is : x / 3 Average of 6 numbers is : (avg. is total /6) (5x+x/3)/6 =10.66 =16X/3 = 64; x = 64*3/16 = 12 6th number is 12 / 3 = 4Ans. . www.afterschoool.tk
A,B,C hire a house for 2 years and agree to pay Rs. 540 as rent p.a. they live for 5 month and C quits, After another 8 months, B quits. Find the rent paid by A.
• Total rent paid = 540*2 = 1080 • Rent paid by C = 540*5/12*1/3 = 75 • Rent paid by B =540*8/12*1/2=180+75= 255 • Rent paid by A = 1080 -75-255 • =1080-330=750Ans.
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DUPLICATE is written as MRVFJFVBE. What is the meaning of CARTOUCHE (for which word is this code used)? If this letter is original word, how will you code it?
• Divide the letter in two parts, and I will be in centre. Reverse each group and add & 2 respectively. Take first 4 digits of code: MRVF, reverse these: FVRM, reduce them as 2,1,2,1,, we get DUPL. Applying the same logic, reverse 1st 4 letters: reduce by 2,1,2,1 TRAC, first letter is RQYBNCGAT. • If the letter is original, then its Code: UTBEPFJDW ans. www.afterschoool.tk
Find three arithmetic means between 5&25? • • • • •
Let us form and AP as 5,A1,A2,A3,25. A + (5-1)D=25; A = 5, D= ? 5D-D=25-5; 4D=20, D = 5, The three means are: 5+5 =10, 10+5 = 15, 15+5 = 20 Ans.
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Find sum of series: 1, -1/3, 1/3^2 , -1/3^3 … to infinity? • Here first term of A = 1. • Dividing second number by first, we get -1 /3, which is ratio of the numbers. The same ratio is there next also. Thus it is GP • GP has same ratio in all its term. • Sum of infinite series = A / (1-r) • =1/ (1- -1/3) = 1/4/3 = ¾ Ans.
www.afterschoool.tk
If ABC are in GP, then Log A, Log B and Log C will be in ? • AP, • Take an example, 10, 100 and 1000 are in GP. Their log values are 1,2,3 – which are in AP. Ans.
www.afterschoool.tk
AM is 34 & GM is 16. What are the numbers?
• Let us assume that two numbers are A & B. Arithmetic mean is to add two numbers and divide by n (2). (a+b)/2 = 34; • A+B = 68. A*B = 16*16 • A-B =square root of [ (A+B)^2 – 4AB] • =[68*68 – 4*256]^1/2= 46241024=3600^1/2=60 • A-B=60; A+B =68, add these 2 equations. • 2A=128, A = 64, B = 4 Ans. www.afterschoool.tk
X:Y = 2:3, Y:Z =4:5, what is X:Y:Z? X:Y = 2:3 , Y: Z = 4:5 Y is common in both, multiply 3*4 = 12. Multiply Y of first with Z of second and get Z = 15, multiply Y of second with X of first and get X = 8. • Ratio of X:Y:Z = 8:12:15 Ans. • • • •
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 • The only absolutely free course on internet • • • • •
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
If A,B,C denote areas of three faces of a cuboid (rectangular faces). What is the volume? • • • • •
Volume = L*B*H L= length, B= bredth, H = height Faces are : L*B, L*H, B*H. Multiplying them together, we have: L^2* B^2*H^2. So the Volume is square root of ABC. Ans.
www.afterschoool.tk
A & B run a 1000 m. race. A gives B a start of 50 meters and still beat him by 1 minute. If A runs @ 8 KM per hour, find B’s speed?
• A’s speed = 8000 m per 60 minutes. • Time take by A = 60*1000/8000 = 7.5 minutes • B ran 950 meters in 8.5 minutes. • Speed of B = 950*60/8.5 = 6706 meters per hours or 6.7 km. per hour (approx. ) ans. www.afterschoool.tk
The average of first 5 numbers is three times the 6th number. If the average of all the 6 numbers is 10.667, find the 6th number? • • • • • • •
Let us assume the average to be x Total of 5 numbers is 5x. 6th number is : x / 3 Average of 6 numbers is : (avg. is total /6) (5x+x/3)/6 =10.66 =16X/3 = 64; x = 64*3/16 = 12 6th number is 12 / 3 = 4Ans. . www.afterschoool.tk
A,B,C hire a house for 2 years and agree to pay Rs. 540 as rent p.a. they live for 5 month and C quits, After another 8 months, B quits. Find the rent paid by A.
• Total rent paid = 540*2 = 1080 • Rent paid by C = 540*5/12*1/3 = 75 • Rent paid by B =540*8/12*1/2=180+75= 255 • Rent paid by A = 1080 -75-255 • =1080-330=750Ans.
www.afterschoool.tk
DUPLICATE is written as MRVFJFVBE. What is the meaning of CARTOUCHE (for which word is this code used)? If this letter is original word, how will you code it?
• Divide the letter in two parts, and I will be in centre. Reverse each group and add & 2 respectively. Take first 4 digits of code: MRVF, reverse these: FVRM, reduce them as 2,1,2,1,, we get DUPL. Applying the same logic, reverse 1st 4 letters: reduce by 2,1,2,1 TRAC, first letter is RQYBNCGAT. • If the letter is original, then its Code: UTBEPFJDW ans. www.afterschoool.tk
Find three arithmetic means between 5&25? • • • • •
Let us form and AP as 5,A1,A2,A3,25. A + (5-1)D=25; A = 5, D= ? 5D-D=25-5; 4D=20, D = 5, The three means are: 5+5 =10, 10+5 = 15, 15+5 = 20 Ans.
www.afterschoool.tk
Find sum of series: 1, -1/3, 1/3^2 , -1/3^3 … to infinity? • Here first term of A = 1. • Dividing second number by first, we get -1 /3, which is ratio of the numbers. The same ratio is there next also. Thus it is GP • GP has same ratio in all its term. • Sum of infinite series = A / (1-r) • =1/ (1- -1/3) = 1/4/3 = ¾ Ans.
www.afterschoool.tk
If ABC are in GP, then Log A, Log B and Log C will be in ? • AP, • Take an example, 10, 100 and 1000 are in GP. Their log values are 1,2,3 – which are in AP. Ans.
www.afterschoool.tk
AM is 34 & GM is 16. What are the numbers?
• Let us assume that two numbers are A & B. Arithmetic mean is to add two numbers and divide by n (2). (a+b)/2 = 34; • A+B = 68. A*B = 16*16 • A-B =square root of [ (A+B)^2 – 4AB] • =[68*68 – 4*256]^1/2= 46241024=3600^1/2=60 • A-B=60; A+B =68, add these 2 equations. • 2A=128, A = 64, B = 4 Ans. www.afterschoool.tk
X:Y = 2:3, Y:Z =4:5, what is X:Y:Z? X:Y = 2:3 , Y: Z = 4:5 Y is common in both, multiply 3*4 = 12. Multiply Y of first with Z of second and get Z = 15, multiply Y of second with X of first and get X = 8. • Ratio of X:Y:Z = 8:12:15 Ans. • • • •
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 • The only absolutely free course on internet • • • • •
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
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