24 June Maths
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Maths Dr. T.K. Jain. AFTERSCHOOOL Centre for social entrepreneurship Bikaner M: 9414430763 [email protected] www.afterschool.tk www.afterschoool.tk www.afterschoool.tk
The sum of the digits of a 2 digit number is 9 and if 9 is added to this number, the digits are reversed. What is the number? Try from options. 45 is the answer (reverse is 54 – which is 9 more then 45. You may also try following equations: X+Y = 9 10X+Y= (10Y+X) - 9
www.afterschoool.tk
The sum of the digits of a 2 digit number is 8 and if 18 is added to this number, the digits are reversed. What is the number? Try from options. 35 is the answer (reverse is 53 – which is 18 more then 35. You may also try following equations: X+Y = 8 10X+Y= (10Y+X) - 18
www.afterschoool.tk
Area of rectangle is 110 sq. meters. If length is increased by 10% and width is reduced by 10%, what will be new area?
Let us assume length and bredth to be 11 & 10. Now we change these: New length: 11+10%=12.1 New width = 10-1 = 9 New area = 12.1*9 =108.9 Note: even if we had reduced length by 10% and increased wideth by 10%, we would have got the same answer. www.afterschoool.tk
Difference between compound interest and simple interest for 2 years is 631. R=10%. What is the sum?
First year’s interest is same. Second year’s interest will be different. In case of compound interest, we charge interest on interest. Thus 631 is interest on interest of 1st year. Thus first year’s interest is 6310. (631*10). Thus principal amount is 63100. www.afterschoool.tk
What is the principal amount which earns 132 as interest in the second year at 10%? (compound interest) Let us take a hypothetical case. If I have Rs. 100 today, I shall get 10 in the first year and I shall get 11 Rs. In 2nd year (10 +1 on interest of first year). Thus principal is : 132 * 100/11 = 1200 answer.
www.afterschoool.tk
I buy bananas @ 9 for Rs. 1.6 and sell them at 11 for Rs. 2. What my gain / loss in %? LCM of 9 & 11 is 99. Suppose I purchased 99 bananas, I paid Rs. 1.6*11=17.6 I sold the same banana : my selling price is : 2*9 = 18. My profit is .4 My profit in % is : .4/17.6 *100=2.27%
www.afterschoool.tk
Cost of 15 bananas is equal to selling price of 20 bananas, what is profit / loss in %? LCM of 15 & 20 is 60. Let 60 be cost of 15 items and selling price of 20 items. The cost price per item is 60/15 = 4 and selling price is Rs. 60/20 = Rs. 3 Thus there is a loss of Re. 1. The loss in percentage is : ¼ *100 = 25% Remember, profit / loss is always calculated with reference to cost.
www.afterschoool.tk
I sold my old car in Rs. 100000 and lost 1/11 in the process. What was my cost?
Let us assume cost to be Re. 1. and loss to be 1/11 (as given). 1-1/11 = 10/11 (thus selling price is 10/11 of cost). In order to get cost, reverse 10/11 and multiply it with selling price. Cost = 100000*11/10 = 110000 answer
www.afterschoool.tk
Cost of 24 bananas is equal to selling price of 18 bananas. What is the profit in %? LCM of 24 & 18 is 72. thus cost of one banana is 72/24 = Rs. 3 and selling price of 1 banana is 72/18 = 4. Profit is 4-3 =1. Thus profit is 1/3 *100 = 33.33%. Answer.
www.afterschoool.tk
A is thrice as good as B in work and completes the work alone in 10 days. In how many days both A & B together can do the same work? A’s one day’s work = 1/10; B’s one day’s work = 1/30 Combine them: 1/10 +1/30 = 40/300 = 1/7.5 Both will be able to complete the work in 7.5 days.
www.afterschoool.tk
A can do a job in 25 days, B can do it in 20 days. A started and B joined after 10 days. When will the work be completed?
A’s 10 days’ work = 1/25*10 = 10/25 or 2/5 Remaining work = 1=2/5 = 3/5 A& B together can do in 1 day: 1/25+1/20 = 45/500 = thus they can complete the work in 500/45 days. They will do 3/5 work in 500/45*3/5 = 6.67 days. Thus total 16.67 days have been taken. www.afterschoool.tk
Angles of quadrilateral are 4:3:6:5, what are the angles? 4+3+6+5 = 18 4/18*360 = 80, 3/18*360 = 60, 6/18*360 = 120 5/18*360 = 100 answer.
www.afterschoool.tk
What is diagonal DB, in ABCE rectangle – if radius of circle is 7 & a is centre point? C D
Obviously 7 ans.
a
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B
A cube’s longest diagonal is 2*3^1/2. what is volume of that cube? Diagonal = side *1.732 Thus side = 2. Volume is side *side *side = 2*2*2 = 8 ans.
www.afterschoool.tk
In 36 minutes, minute hand gains over hour hand by ? Hour hand covers 5 minutes in 60 minutes. Thus it will cover 5/60 *36 = 3 minutes. Thus 36-3 =33 answer
www.afterschoool.tk
At what time, will there be right angle between 9 & 10? (in 2 hands) There are 2 such occasions: at 9 and at somewhere after 30 minutes after 9. Instead of 30 minutes, we will take 30 * 60/55 = 32.72 Thus there will be right angle at 9 and at 9 hours and 32.72 minutes. Since 9 is not included in the question, so answer is 9 h.32.72 minutes.
www.afterschoool.tk
At what time, will there be right angle between 10 & 11? (in 2 hands)
There are 2 such occasions: at 10h 10m and at somewhere after 40 minutes after 10. Instead of 10 & 40 minutes, we will multiply these by * 60/55 = 10.09 & 43.63 So answer: 10 hours and 10.09 minutes and 43.63 minutes.
www.afterschoool.tk
If the 2 hands of my watch coinside every 60 minutes, is it on time or not? The 2 hands should coinside after 60 *60/55 minutes = 65.45 minutes. Thus my watch is fast by 5.45 minutes or fast by 5 minutes and 27 seconds. 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
Why such a programme?
To promote people to take up entrepreneurship and help develop the society To enable people to take up franchising and other such options to start a business / social development project To enable people to take up social development as their mission To enable people to promote spirituality and positive thinking in the world www.afterschoool.tk
Who are our supporters? Afterschoolians, our past beneficiaries, entrepreneurs and social entrepreneurs are supporting us. You can also support us – not necessarily by money – but by being promotor of our concept and our ideas.
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, BPO, KPO Accounting & Information system (with CA / CS /CMA) 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 Admissions open throughout the year Latest and most advanced technologies, books and study material
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 Participation in conferences and seminars Group discussions, mock interviews, self development diaryng Mind Power Training & writing workshop (by Dr. T.K.Jain)
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 Study exchange programme (with institutions out of India) Rural development / Social welfare projects
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
The sum of the digits of a 2 digit number is 9 and if 9 is added to this number, the digits are reversed. What is the number? Try from options. 45 is the answer (reverse is 54 – which is 9 more then 45. You may also try following equations: X+Y = 9 10X+Y= (10Y+X) - 9
www.afterschoool.tk
The sum of the digits of a 2 digit number is 8 and if 18 is added to this number, the digits are reversed. What is the number? Try from options. 35 is the answer (reverse is 53 – which is 18 more then 35. You may also try following equations: X+Y = 8 10X+Y= (10Y+X) - 18
www.afterschoool.tk
Area of rectangle is 110 sq. meters. If length is increased by 10% and width is reduced by 10%, what will be new area?
Let us assume length and bredth to be 11 & 10. Now we change these: New length: 11+10%=12.1 New width = 10-1 = 9 New area = 12.1*9 =108.9 Note: even if we had reduced length by 10% and increased wideth by 10%, we would have got the same answer. www.afterschoool.tk
Difference between compound interest and simple interest for 2 years is 631. R=10%. What is the sum?
First year’s interest is same. Second year’s interest will be different. In case of compound interest, we charge interest on interest. Thus 631 is interest on interest of 1st year. Thus first year’s interest is 6310. (631*10). Thus principal amount is 63100. www.afterschoool.tk
What is the principal amount which earns 132 as interest in the second year at 10%? (compound interest) Let us take a hypothetical case. If I have Rs. 100 today, I shall get 10 in the first year and I shall get 11 Rs. In 2nd year (10 +1 on interest of first year). Thus principal is : 132 * 100/11 = 1200 answer.
www.afterschoool.tk
I buy bananas @ 9 for Rs. 1.6 and sell them at 11 for Rs. 2. What my gain / loss in %? LCM of 9 & 11 is 99. Suppose I purchased 99 bananas, I paid Rs. 1.6*11=17.6 I sold the same banana : my selling price is : 2*9 = 18. My profit is .4 My profit in % is : .4/17.6 *100=2.27%
www.afterschoool.tk
Cost of 15 bananas is equal to selling price of 20 bananas, what is profit / loss in %? LCM of 15 & 20 is 60. Let 60 be cost of 15 items and selling price of 20 items. The cost price per item is 60/15 = 4 and selling price is Rs. 60/20 = Rs. 3 Thus there is a loss of Re. 1. The loss in percentage is : ¼ *100 = 25% Remember, profit / loss is always calculated with reference to cost.
www.afterschoool.tk
I sold my old car in Rs. 100000 and lost 1/11 in the process. What was my cost?
Let us assume cost to be Re. 1. and loss to be 1/11 (as given). 1-1/11 = 10/11 (thus selling price is 10/11 of cost). In order to get cost, reverse 10/11 and multiply it with selling price. Cost = 100000*11/10 = 110000 answer
www.afterschoool.tk
Cost of 24 bananas is equal to selling price of 18 bananas. What is the profit in %? LCM of 24 & 18 is 72. thus cost of one banana is 72/24 = Rs. 3 and selling price of 1 banana is 72/18 = 4. Profit is 4-3 =1. Thus profit is 1/3 *100 = 33.33%. Answer.
www.afterschoool.tk
A is thrice as good as B in work and completes the work alone in 10 days. In how many days both A & B together can do the same work? A’s one day’s work = 1/10; B’s one day’s work = 1/30 Combine them: 1/10 +1/30 = 40/300 = 1/7.5 Both will be able to complete the work in 7.5 days.
www.afterschoool.tk
A can do a job in 25 days, B can do it in 20 days. A started and B joined after 10 days. When will the work be completed?
A’s 10 days’ work = 1/25*10 = 10/25 or 2/5 Remaining work = 1=2/5 = 3/5 A& B together can do in 1 day: 1/25+1/20 = 45/500 = thus they can complete the work in 500/45 days. They will do 3/5 work in 500/45*3/5 = 6.67 days. Thus total 16.67 days have been taken. www.afterschoool.tk
Angles of quadrilateral are 4:3:6:5, what are the angles? 4+3+6+5 = 18 4/18*360 = 80, 3/18*360 = 60, 6/18*360 = 120 5/18*360 = 100 answer.
www.afterschoool.tk
What is diagonal DB, in ABCE rectangle – if radius of circle is 7 & a is centre point? C D
Obviously 7 ans.
a
www.afterschoool.tk
B
A cube’s longest diagonal is 2*3^1/2. what is volume of that cube? Diagonal = side *1.732 Thus side = 2. Volume is side *side *side = 2*2*2 = 8 ans.
www.afterschoool.tk
In 36 minutes, minute hand gains over hour hand by ? Hour hand covers 5 minutes in 60 minutes. Thus it will cover 5/60 *36 = 3 minutes. Thus 36-3 =33 answer
www.afterschoool.tk
At what time, will there be right angle between 9 & 10? (in 2 hands) There are 2 such occasions: at 9 and at somewhere after 30 minutes after 9. Instead of 30 minutes, we will take 30 * 60/55 = 32.72 Thus there will be right angle at 9 and at 9 hours and 32.72 minutes. Since 9 is not included in the question, so answer is 9 h.32.72 minutes.
www.afterschoool.tk
At what time, will there be right angle between 10 & 11? (in 2 hands)
There are 2 such occasions: at 10h 10m and at somewhere after 40 minutes after 10. Instead of 10 & 40 minutes, we will multiply these by * 60/55 = 10.09 & 43.63 So answer: 10 hours and 10.09 minutes and 43.63 minutes.
www.afterschoool.tk
If the 2 hands of my watch coinside every 60 minutes, is it on time or not? The 2 hands should coinside after 60 *60/55 minutes = 65.45 minutes. Thus my watch is fast by 5.45 minutes or fast by 5 minutes and 27 seconds. 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
Why such a programme?
To promote people to take up entrepreneurship and help develop the society To enable people to take up franchising and other such options to start a business / social development project To enable people to take up social development as their mission To enable people to promote spirituality and positive thinking in the world www.afterschoool.tk
Who are our supporters? Afterschoolians, our past beneficiaries, entrepreneurs and social entrepreneurs are supporting us. You can also support us – not necessarily by money – but by being promotor of our concept and our ideas.
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, BPO, KPO Accounting & Information system (with CA / CS /CMA) 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 Admissions open throughout the year Latest and most advanced technologies, books and study material
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 Participation in conferences and seminars Group discussions, mock interviews, self development diaryng Mind Power Training & writing workshop (by Dr. T.K.Jain)
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 Study exchange programme (with institutions out of India) Rural development / Social welfare projects
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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