16 June Maths Iv
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MATHS Dr. T.K. Jain. AFTERSCHOOOL M: 9414430763 [email protected] www.afterschool.tk www.afterschoool.tk
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4 Pipes can fill a reservoir in 15, 20, 30 & 60 hours. The first was opened at 6 am, 2nd at 7 am, 3rd at 8 am and 4th at 9 am. When will the reservoir be filled up? • Till 9 am all have different timings. • We have therefore : 3/15 +2/20 +1/30. = 20/60 or 1/3 • From 9 they are all opened so let us find their total time: 1/15 +1/20 +1/30+1/60 = 10/60 or 6 hours. • Total is filled in 6 hours, 2/3 will be filled in 6*2/3 = 4 hours. Thus reservoir will be filled at 1 pm. Ans.
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A man possessing Rs. 8400 lent a part of it at 8% and remaining at 6.66%. His total income after 1.5 years was 882. Find the sum lent at 6.66% rate? • His annual return is 882*2/3*1/8400 =7% • Thus ratio is 1:3 • Sum lent at 6.66% is ¾ * 8400 • = 6300 ans.
Rate
8 .33
www.afterschoool.tk
7
6.66 1
The average of the squares of 7 consecutive integers is 53. the average of these integers is ?
• Total of squares is 53*7 = 371 • Solve it by options, we have to get the values near by 7-8 (square root of 53). Try with 4,5,6,7,8,9, 10. Add 16,25,36,49, 64, 81, 100, we get the answer.
www.afterschoool.tk
A positive number decreased by 4 is equal to 21 times the reciprocal of the number. What is the number?
• • • • • •
Let us assume the number to be X. X – 4 = 21 (1/X) X^2 – 4X -21 = 0 X^2 -7X+3X -21 = 0 X(X-7) + 3(X-7) = 0 Thus X = 7. www.afterschoool.tk
If market price of pen drive is 700 and 2 successive discounts are given at 15% & 20%. What is effective discount rate & how much money will you pay?
• Let us take first discount 100 – 15 = 85. now take 20% of 85, we get 17. 85-17 = 68 • Thus effective discount rate is 100 – 68 = 32 % ans. • 700*68/100= 476 ans.
www.afterschoool.tk
Find the area of quadrant, if radius is 6? • Pi * 6*6*1/4 • =22/7*9 • =28 approx.
www.afterschoool.tk
Find the geometric progression, whose sum to infinity is 9/2 and 2nd term is -2? • Formulae is a / (1-r); a = first term • R = ratio of two terms • Second term is called A*R = AR • First term will be AR / R or -2 / R -2 / r * 1/(1-r) = 9/2 9R – 9R^2 = -4; or 9r^2 -9r -4 = 0 Divide equation by 9, = r^2 – r – 4/9 =0 R^2 – 4/3 r + 1/3 r – 4/9 = 0 R (r-4/3) +1/3 (r-4/3) = 0 R = 4/3 or -1/3 ; thus first term is -2 / -1/3 = 6 Series is 6, -2, 1/3, -1/9 answer.
www.afterschoool.tk
No. of bacteria triple every minute. Initially there are 100 bacteria at the end of 1st minute. What will be number of bacteria after 4 minutes?
• • • • • •
Formulae is AR ^ (n-1) A = 100 R=3 N=4 100*3^3 =2700 answer. www.afterschoool.tk
Find the sum of first 10 terms in the series 5, 5.5, 5.55, 5.555 … ? • We can write this series as 5( 1, 1.1, 1.11, 1.111…) • We can add the insider series as : • (10-1)/9, (10-.1)/9 … so on. Now take 9 as common. Now we have 2 series: • (10*10) = 100, (1+.1+.01 ..) the second series is GP. A * (1-r ^n) / (1-r) • =(1 *.999999999)/.9 = 1.11 • 100 – 1.11 = 98.89 multiplied by 5/9 = • =98.89 *5/9 = 54.9 answer
www.afterschoool.tk
ABOUT AFTERSCHOOOL Afterschoool conducts three year integrated PGPSE (after class 12th 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
Flexible 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 want to achieve success in life – not just a degree • Indepth knowledge and expertise • Professional approac: World class approach • Strong intellectual and business capabilities • Flexible – you may stay for a month and continue the rest of the education by distance mode. • Scholarships for those from poor economic background • Latest and constantly changing curriculum – keeping pace with the time • Placement for those who are interested
www.afterschoool.tk
Components • • • • • • • • • • •
Pedagogy curriculum and approach based on IIM Ahmedabad and ISB Hyderabad (the founder is alumnus from IIMA & ISB Hyderabad) Meditation, spiritualisation, and self development Essential softwares for business Business plan, 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
Branches • AFTERSCHOOOL will shortly open its branches in important cities in India including Delhi, Kota, Mumbai, Gurgaon and other important cities. Afterschooolians will be responsible for managing and developing these branches – and for promoting social entrepreneurs. www.afterschoool.tk
Case Studies • We want to write case studies on social entrepreneurs, first generation entrepreneurs, ethical entrepreneurs. Please help us in this process. Help us to be in touch with entrepreneurs, so that we may develop entrepreneurs. www.afterschoool.tk
www.afterschoool.tk social entrepreneurship for better society
www.afterschoool.tk
www.afterschoool.tk
4 Pipes can fill a reservoir in 15, 20, 30 & 60 hours. The first was opened at 6 am, 2nd at 7 am, 3rd at 8 am and 4th at 9 am. When will the reservoir be filled up? • Till 9 am all have different timings. • We have therefore : 3/15 +2/20 +1/30. = 20/60 or 1/3 • From 9 they are all opened so let us find their total time: 1/15 +1/20 +1/30+1/60 = 10/60 or 6 hours. • Total is filled in 6 hours, 2/3 will be filled in 6*2/3 = 4 hours. Thus reservoir will be filled at 1 pm. Ans.
www.afterschoool.tk
A man possessing Rs. 8400 lent a part of it at 8% and remaining at 6.66%. His total income after 1.5 years was 882. Find the sum lent at 6.66% rate? • His annual return is 882*2/3*1/8400 =7% • Thus ratio is 1:3 • Sum lent at 6.66% is ¾ * 8400 • = 6300 ans.
Rate
8 .33
www.afterschoool.tk
7
6.66 1
The average of the squares of 7 consecutive integers is 53. the average of these integers is ?
• Total of squares is 53*7 = 371 • Solve it by options, we have to get the values near by 7-8 (square root of 53). Try with 4,5,6,7,8,9, 10. Add 16,25,36,49, 64, 81, 100, we get the answer.
www.afterschoool.tk
A positive number decreased by 4 is equal to 21 times the reciprocal of the number. What is the number?
• • • • • •
Let us assume the number to be X. X – 4 = 21 (1/X) X^2 – 4X -21 = 0 X^2 -7X+3X -21 = 0 X(X-7) + 3(X-7) = 0 Thus X = 7. www.afterschoool.tk
If market price of pen drive is 700 and 2 successive discounts are given at 15% & 20%. What is effective discount rate & how much money will you pay?
• Let us take first discount 100 – 15 = 85. now take 20% of 85, we get 17. 85-17 = 68 • Thus effective discount rate is 100 – 68 = 32 % ans. • 700*68/100= 476 ans.
www.afterschoool.tk
Find the area of quadrant, if radius is 6? • Pi * 6*6*1/4 • =22/7*9 • =28 approx.
www.afterschoool.tk
Find the geometric progression, whose sum to infinity is 9/2 and 2nd term is -2? • Formulae is a / (1-r); a = first term • R = ratio of two terms • Second term is called A*R = AR • First term will be AR / R or -2 / R -2 / r * 1/(1-r) = 9/2 9R – 9R^2 = -4; or 9r^2 -9r -4 = 0 Divide equation by 9, = r^2 – r – 4/9 =0 R^2 – 4/3 r + 1/3 r – 4/9 = 0 R (r-4/3) +1/3 (r-4/3) = 0 R = 4/3 or -1/3 ; thus first term is -2 / -1/3 = 6 Series is 6, -2, 1/3, -1/9 answer.
www.afterschoool.tk
No. of bacteria triple every minute. Initially there are 100 bacteria at the end of 1st minute. What will be number of bacteria after 4 minutes?
• • • • • •
Formulae is AR ^ (n-1) A = 100 R=3 N=4 100*3^3 =2700 answer. www.afterschoool.tk
Find the sum of first 10 terms in the series 5, 5.5, 5.55, 5.555 … ? • We can write this series as 5( 1, 1.1, 1.11, 1.111…) • We can add the insider series as : • (10-1)/9, (10-.1)/9 … so on. Now take 9 as common. Now we have 2 series: • (10*10) = 100, (1+.1+.01 ..) the second series is GP. A * (1-r ^n) / (1-r) • =(1 *.999999999)/.9 = 1.11 • 100 – 1.11 = 98.89 multiplied by 5/9 = • =98.89 *5/9 = 54.9 answer
www.afterschoool.tk
ABOUT AFTERSCHOOOL Afterschoool conducts three year integrated PGPSE (after class 12th 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
Flexible 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 want to achieve success in life – not just a degree • Indepth knowledge and expertise • Professional approac: World class approach • Strong intellectual and business capabilities • Flexible – you may stay for a month and continue the rest of the education by distance mode. • Scholarships for those from poor economic background • Latest and constantly changing curriculum – keeping pace with the time • Placement for those who are interested
www.afterschoool.tk
Components • • • • • • • • • • •
Pedagogy curriculum and approach based on IIM Ahmedabad and ISB Hyderabad (the founder is alumnus from IIMA & ISB Hyderabad) Meditation, spiritualisation, and self development Essential softwares for business Business plan, 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
Branches • AFTERSCHOOOL will shortly open its branches in important cities in India including Delhi, Kota, Mumbai, Gurgaon and other important cities. Afterschooolians will be responsible for managing and developing these branches – and for promoting social entrepreneurs. www.afterschoool.tk
Case Studies • We want to write case studies on social entrepreneurs, first generation entrepreneurs, ethical entrepreneurs. Please help us in this process. Help us to be in touch with entrepreneurs, so that we may develop entrepreneurs. www.afterschoool.tk
www.afterschoool.tk social entrepreneurship for better society
www.afterschoool.tk
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