17 June Maths Ii
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MATHS Dr. T.K. Jain. AFTERSCHOOOL M: 9414430763 [email protected] www.afterschool.tk www.afterschoool.tk
www.afterschoool.tk
What is value of log
10
100
• We know that 10^2 = 100 • Therefore the answer is 2.
www.afterschoool.tk
?
What is log
8
128
8^X = 128 (2^3)^X = 2^7 Let us take 2 common. 3X = 7 X = 7/3 • log 8 128 = 7/3 • • • • •
www.afterschoool.tk
?
What is log
85498
85498
• 1 ans.
www.afterschoool.tk
?
What is the value of Rs. 8000 invested at 20% compound interest compounded quarterly for 4 years?
• Interest is compounded quarterly, so we will calculate interest @ 5%. • Re. 1 will be 1.05 after first quarter and will be 105 *1.05 after 2nd quarter. • Thus 8000*1.05^16 ans. • = 17463 ans. www.afterschoool.tk
Population of Bikaner is 550000 now. It increased @10%, 15% & 12% during last 3 years. What was the population 3 years back? • Let us assume that population 3 years back was X. It increased @ 10% - it became 1.1X, then it increased @15%, and it became 1.15*1.1X and it again increased. So today’s population is : • 1.12*1.15*1.1X = 550000 • X = 550000 / (1.12*1.15*1.1) =388200 Ans.
www.afterschoool.tk
I want to buy a readymade shirt in Bikaner. Shops are giving following discounts for same shirt:1. (50% +50%) 2. 40% + 60% 3. 20% +20% + 61% 4. 90%+5%. Which is better?
• • • • • •
Let us evaluate these: 1. 1*.5 = .5 *.5 = .25 2. 1*.6 = .6 *.4 = .24 3. 1*.8 = .8 *.8= .64 *.39 =.2496 4. 1*.1 = .1*.95 = .095 Thus 4th option is the best. www.afterschoool.tk
A shopkeeper uses 800 grams weight for selling 1Kg and sells at the print rate. He buys at print rate, but while buying, he uses 1200 grams instead of 1000 gram for 1KG. What is his profit in %?
• Let us take LCM of 8& 12 = 24. Let us assume that he purchased 2400 grams. Let us say print price is 1 per kg. Shopkeeper paid Rs. 2 (2400 gram is 2 kg while purchasing). He sold and got Rs. 3 (2400 grams are equal to 3 Kg for selling). Thus his profit is 50%. www.afterschoool.tk
On my bike I travel 100 Km in 3 hours. How much will I travel on Bitthal’s bike in 10 hours, if Bitthal drives at double the speed?
• 666.66 Km.
www.afterschoool.tk
Bitthal covers 4 successive equal stretches with a speeds of 20,30,40,60. What is average speed of Bitthal?
• It is a question of harmonic mean. Let us calculate harmonic mean. • 1/20 +1/30 + 1/40 +1/60 = (6+4+3+2) / 120 = 15 /120 multiply it by ¼ = 15/480 • Thus average speed is 480/15 = 32 k.m. per hour. Answer.
www.afterschoool.tk
The distance between AFTERSCHOOOL & Devendra’s house is 5 Km. what should be speed to cover this distance in 10 minutes. Out of these 5 KM. we cant have speed of over 20 for 2KM.
• Total time for 2 km (speed is 20). = 6 minuts • We have to cover 3 KM in 4 minutes. • ¾ * 60 = 45 KM per hour. • Average speed is total distance / total time • = 5 /10/60 = 30 KM per hour. www.afterschoool.tk
Put these in descending order: 12/47, 4/15, 21/60? • Descending order means first the biggest, then smallers in succession. • Let us multiply 15*60 to 12, and 47*60 to 4 and 47*15 to 21 and get the answers. • 10800, 11280, 14805. • Thus the correct order is 21/60, 4/15 & 12/47 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. / you may attend weekend classes • 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, Articles from Harvard Business Review Quiz, seminars, workshops, games, Visits to entrepreneurs and industrial visits Presentations, Latest audio-visuals 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
Basic values at afterschoool Share to learn more Interact to develop yourself Fear is your worst enemy Make mistakes to learn Study & discuss in a group Criticism is the healthy route to mutual support and help • Ask fundamental questions : why, when, how & where? • Embrace change – and compete with yourself only • • • • • •
www.afterschoool.tk
www.afterschoool.tk social entrepreneurship for better society
www.afterschoool.tk
www.afterschoool.tk
What is value of log
10
100
• We know that 10^2 = 100 • Therefore the answer is 2.
www.afterschoool.tk
?
What is log
8
128
8^X = 128 (2^3)^X = 2^7 Let us take 2 common. 3X = 7 X = 7/3 • log 8 128 = 7/3 • • • • •
www.afterschoool.tk
?
What is log
85498
85498
• 1 ans.
www.afterschoool.tk
?
What is the value of Rs. 8000 invested at 20% compound interest compounded quarterly for 4 years?
• Interest is compounded quarterly, so we will calculate interest @ 5%. • Re. 1 will be 1.05 after first quarter and will be 105 *1.05 after 2nd quarter. • Thus 8000*1.05^16 ans. • = 17463 ans. www.afterschoool.tk
Population of Bikaner is 550000 now. It increased @10%, 15% & 12% during last 3 years. What was the population 3 years back? • Let us assume that population 3 years back was X. It increased @ 10% - it became 1.1X, then it increased @15%, and it became 1.15*1.1X and it again increased. So today’s population is : • 1.12*1.15*1.1X = 550000 • X = 550000 / (1.12*1.15*1.1) =388200 Ans.
www.afterschoool.tk
I want to buy a readymade shirt in Bikaner. Shops are giving following discounts for same shirt:1. (50% +50%) 2. 40% + 60% 3. 20% +20% + 61% 4. 90%+5%. Which is better?
• • • • • •
Let us evaluate these: 1. 1*.5 = .5 *.5 = .25 2. 1*.6 = .6 *.4 = .24 3. 1*.8 = .8 *.8= .64 *.39 =.2496 4. 1*.1 = .1*.95 = .095 Thus 4th option is the best. www.afterschoool.tk
A shopkeeper uses 800 grams weight for selling 1Kg and sells at the print rate. He buys at print rate, but while buying, he uses 1200 grams instead of 1000 gram for 1KG. What is his profit in %?
• Let us take LCM of 8& 12 = 24. Let us assume that he purchased 2400 grams. Let us say print price is 1 per kg. Shopkeeper paid Rs. 2 (2400 gram is 2 kg while purchasing). He sold and got Rs. 3 (2400 grams are equal to 3 Kg for selling). Thus his profit is 50%. www.afterschoool.tk
On my bike I travel 100 Km in 3 hours. How much will I travel on Bitthal’s bike in 10 hours, if Bitthal drives at double the speed?
• 666.66 Km.
www.afterschoool.tk
Bitthal covers 4 successive equal stretches with a speeds of 20,30,40,60. What is average speed of Bitthal?
• It is a question of harmonic mean. Let us calculate harmonic mean. • 1/20 +1/30 + 1/40 +1/60 = (6+4+3+2) / 120 = 15 /120 multiply it by ¼ = 15/480 • Thus average speed is 480/15 = 32 k.m. per hour. Answer.
www.afterschoool.tk
The distance between AFTERSCHOOOL & Devendra’s house is 5 Km. what should be speed to cover this distance in 10 minutes. Out of these 5 KM. we cant have speed of over 20 for 2KM.
• Total time for 2 km (speed is 20). = 6 minuts • We have to cover 3 KM in 4 minutes. • ¾ * 60 = 45 KM per hour. • Average speed is total distance / total time • = 5 /10/60 = 30 KM per hour. www.afterschoool.tk
Put these in descending order: 12/47, 4/15, 21/60? • Descending order means first the biggest, then smallers in succession. • Let us multiply 15*60 to 12, and 47*60 to 4 and 47*15 to 21 and get the answers. • 10800, 11280, 14805. • Thus the correct order is 21/60, 4/15 & 12/47 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. / you may attend weekend classes • 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, Articles from Harvard Business Review Quiz, seminars, workshops, games, Visits to entrepreneurs and industrial visits Presentations, Latest audio-visuals 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
Basic values at afterschoool Share to learn more Interact to develop yourself Fear is your worst enemy Make mistakes to learn Study & discuss in a group Criticism is the healthy route to mutual support and help • Ask fundamental questions : why, when, how & where? • Embrace change – and compete with yourself only • • • • • •
www.afterschoool.tk
www.afterschoool.tk social entrepreneurship for better society
www.afterschoool.tk
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