10 June Maths Iii
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Maths Dr. T.K. Jain. AFTERSCHOOOL M: 9414430763 [email protected] www.afterschool.tk www.afterschoool.tk
www.afterschoool.tk
A tree of 121 meters height break from somewhere in the middle and falls on the ground. The other portion touches ground at a distance of 11 meters from the trunk of tree. 11 What is the height of tree now?
• Let us assume the height of tree is X. • The other portion of tree is 121-x • We know that X^2 + 11^2 = (121-x)^2 • X^2 +11^2=14641-242x+x^2 • 242X = 14641-121; X= 14520/242 = 60 M. www.afterschoool.tk
Monthly salaries of 2 persons are in ratio 3:5. If each receives an increment of Rs. 20 in salary, the new ratio becomes 13:21. What was initial salary? • Let us assume that their initial salaries are 3X and 5 X. • As per the question: (3X+20 )*21 = (5x +20) *13 • 63X +420=65X +260 • 2X= 160; X = 80 • Initial Salaries are (3X) 240 and (5X) 400 answer.
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A,B,C start partnership firm. A contributes 16000. Out of profit of 14400, A gets 3840 and B gets 5760. What was the money invested by C?
• C gets =14400 -3840-5760= 4800 • Now we will compare C’s share with A’s and find his capital according to the ratio of their profit sharing ratio • C’s capital is: • 4800/3840 *16000 =20000
www.afterschoool.tk
Ram goes 9 Km to the West then turned right and traelled 7 Km. then turned left and travelled 8 Km. then turned back and travelled 11 Km. the turned right and travelled 7 Km. How far and in which direction is he from the start?
• •
8 7
11 km 3 7
6 Km
Start
9 Km
• He is 6 Km west from starting point. www.afterschoool.tk
A walks 10 m. in front. And 10 m. to the right. Then every time turning left he walks 5,15 &15 meters respectively. How far is he from starting point?
• 5 meters.
www.afterschoool.tk
I am walking towards East. Mention three steps through which I turn to South? Options: 1. LLL 2. RRR 3. LLR 4. LRL 5. RLR
• Two Left turns will make me west facing another left turn will make me south facing – so answer is LLL or left left and left turn. • RLR will also make us south facing and give us the answer. One R and one L will get cancelled. One R will take us towards south. www.afterschoool.tk
Two taps can separately fill a cistern in 6 & 7 minutes. If the taps are opened turn by turn each for 1 minute. When will the cistern be filled? • The taps fill alternately. Let us assume that if they are opened together what will happen. First fill up in 1 minute = 1/6 and 2nd will fill up 1/7 in 1 minute. • 1/6 +1/7 = 13/42 reverse 42/13 = 3. something. • That means each tap will be opened for 3 minutes at least. • 3/6 + 3/7 will give us 39/42. now 3/42 is left. Now first tap will be opened again. 6*3/42 will give us 3/7 minutes • Thus total time = 6 minutes and 3/7 minutes ans.
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2 men and 3 women working 7 hours a day finish a work in 5 days. 4 men and 4 women working 3 hours a day do the same in 7 days. Find the number of days in which the work is done by 7 men only working 4 hours a day.
• 2x+3y =1/35; 4x+4y= 1/21 • Solving these equations, (multiply first equation by 4 and 2nd by 3). • -4x = 4/35-3/21 ; 4x =3/105 • X=1/140. • 140 / (7*4) = 5 • Thus it will take 5 days. www.afterschoool.tk
10 men, 10 boys, 5 women can do some work in 30 days. The capacity of one man is equal to 2 boys and capacity of 2 men are equal to 3 women. Work was started and after 10 days 10 mre boys 10 men and 5 women joined. In how many days work will be completed?
• In 10 days 1/3rd work is completed. • After 10 days, we have additional reinforcement of same manpower. These people will have double the capacity to work and so they will do the remaining work in half the time. The remaining work is of 20 days, but they will do it in 10 days. Thus total work will be finished in 20 days. www.afterschoool.tk
Two coins are tossed simultaneously, what is the probability of getting at least 1 head?
• Total chances are : 2*2 = 4 • All chances are as under: • HT,TH,TT,HH (there are three possibilities with at least one head). • The chances of getting at lest one head is ¾ (solve by observation). • Ans. www.afterschoool.tk
AM of 25 numbers is 36. AM of first 13 numbers is 32 and that of last 13 numbers is 39. what is 13th number?
• • • • •
Total is 25*36 =900 Total of 1st 13th numbers = 13*32=416 Total of last 13 is 13*39 = 507 Total of these numbers is 507+416 = 923 the 13th number is 923-900 = 23 ans.
www.afterschoool.tk
I have to take weights from 1 to 121. What is the minimum number of weights that I should keep to weigh all these?
• Start from 1, 3, 9,27,81 • Thus we require only 5 weights to weigh these weights.
www.afterschoool.tk
Thanks 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
A tree of 121 meters height break from somewhere in the middle and falls on the ground. The other portion touches ground at a distance of 11 meters from the trunk of tree. 11 What is the height of tree now?
• Let us assume the height of tree is X. • The other portion of tree is 121-x • We know that X^2 + 11^2 = (121-x)^2 • X^2 +11^2=14641-242x+x^2 • 242X = 14641-121; X= 14520/242 = 60 M. www.afterschoool.tk
Monthly salaries of 2 persons are in ratio 3:5. If each receives an increment of Rs. 20 in salary, the new ratio becomes 13:21. What was initial salary? • Let us assume that their initial salaries are 3X and 5 X. • As per the question: (3X+20 )*21 = (5x +20) *13 • 63X +420=65X +260 • 2X= 160; X = 80 • Initial Salaries are (3X) 240 and (5X) 400 answer.
www.afterschoool.tk
A,B,C start partnership firm. A contributes 16000. Out of profit of 14400, A gets 3840 and B gets 5760. What was the money invested by C?
• C gets =14400 -3840-5760= 4800 • Now we will compare C’s share with A’s and find his capital according to the ratio of their profit sharing ratio • C’s capital is: • 4800/3840 *16000 =20000
www.afterschoool.tk
Ram goes 9 Km to the West then turned right and traelled 7 Km. then turned left and travelled 8 Km. then turned back and travelled 11 Km. the turned right and travelled 7 Km. How far and in which direction is he from the start?
• •
8 7
11 km 3 7
6 Km
Start
9 Km
• He is 6 Km west from starting point. www.afterschoool.tk
A walks 10 m. in front. And 10 m. to the right. Then every time turning left he walks 5,15 &15 meters respectively. How far is he from starting point?
• 5 meters.
www.afterschoool.tk
I am walking towards East. Mention three steps through which I turn to South? Options: 1. LLL 2. RRR 3. LLR 4. LRL 5. RLR
• Two Left turns will make me west facing another left turn will make me south facing – so answer is LLL or left left and left turn. • RLR will also make us south facing and give us the answer. One R and one L will get cancelled. One R will take us towards south. www.afterschoool.tk
Two taps can separately fill a cistern in 6 & 7 minutes. If the taps are opened turn by turn each for 1 minute. When will the cistern be filled? • The taps fill alternately. Let us assume that if they are opened together what will happen. First fill up in 1 minute = 1/6 and 2nd will fill up 1/7 in 1 minute. • 1/6 +1/7 = 13/42 reverse 42/13 = 3. something. • That means each tap will be opened for 3 minutes at least. • 3/6 + 3/7 will give us 39/42. now 3/42 is left. Now first tap will be opened again. 6*3/42 will give us 3/7 minutes • Thus total time = 6 minutes and 3/7 minutes ans.
www.afterschoool.tk
2 men and 3 women working 7 hours a day finish a work in 5 days. 4 men and 4 women working 3 hours a day do the same in 7 days. Find the number of days in which the work is done by 7 men only working 4 hours a day.
• 2x+3y =1/35; 4x+4y= 1/21 • Solving these equations, (multiply first equation by 4 and 2nd by 3). • -4x = 4/35-3/21 ; 4x =3/105 • X=1/140. • 140 / (7*4) = 5 • Thus it will take 5 days. www.afterschoool.tk
10 men, 10 boys, 5 women can do some work in 30 days. The capacity of one man is equal to 2 boys and capacity of 2 men are equal to 3 women. Work was started and after 10 days 10 mre boys 10 men and 5 women joined. In how many days work will be completed?
• In 10 days 1/3rd work is completed. • After 10 days, we have additional reinforcement of same manpower. These people will have double the capacity to work and so they will do the remaining work in half the time. The remaining work is of 20 days, but they will do it in 10 days. Thus total work will be finished in 20 days. www.afterschoool.tk
Two coins are tossed simultaneously, what is the probability of getting at least 1 head?
• Total chances are : 2*2 = 4 • All chances are as under: • HT,TH,TT,HH (there are three possibilities with at least one head). • The chances of getting at lest one head is ¾ (solve by observation). • Ans. www.afterschoool.tk
AM of 25 numbers is 36. AM of first 13 numbers is 32 and that of last 13 numbers is 39. what is 13th number?
• • • • •
Total is 25*36 =900 Total of 1st 13th numbers = 13*32=416 Total of last 13 is 13*39 = 507 Total of these numbers is 507+416 = 923 the 13th number is 923-900 = 23 ans.
www.afterschoool.tk
I have to take weights from 1 to 121. What is the minimum number of weights that I should keep to weigh all these?
• Start from 1, 3, 9,27,81 • Thus we require only 5 weights to weigh these weights.
www.afterschoool.tk
Thanks 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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