16 June Maths Iii
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MATHS Dr. T.K. Jain. AFTERSCHOOOL M: 9414430763 [email protected] www.afterschool.tk www.afterschoool.tk
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A clock is set right at 1 pm. It gains 1 min. per hour. What is the true time when the clock shows 6 pm on the same day? • The clock gains 1 minutes per hour – it is faster then the time. Difference of 6 & 1 is 5 hours. We know that when the real difference is 60 minutes, clock shows difference of 61 minutes. Applying the same principle, 60/61 * 300 = 295. 08 that means the real time must be 5.55.08 at that time approx.
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A vessel weights 16.5 KG when it is full of water. When it is 1/4th full, the weight is 5.25 kg. what is the weight of empty vessel? • Let us assume that weight of vessel is X kg & the material inside weighs Y kg. • X + Y = 16.5 ; X + .25 Y = 5.25; let us multiply 2nd equation with 4. Now it becomes: 4 X + Y = 21 • Deducting 2nd equation from 1st equation, we get: • 3X = 4.5 or X = 1.5 KG. answer. • .
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In 15 days 9 men and 15 boys can reap a field. In what time could 15 men and 16 boys reap the field assuming 3 men can do as much as 4 boys?
• Convert men into boys. Thus we have 12 + 15 (27) boys doing work in 15 days. • Now we have 20 (15 men are equal to 20 boys) and 16 boys working (total 36 boys). • Applying our trick, solve it as : • 15 * 27 / 36 = 11.25 days.
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2 taps A & B can fill a tank in 12 & 16 minutes respectively. Both are kept open for X minutes then B is closed. A fills up the rest of tank in 5 minutes. What is X ? • We know that A can fill up 1/12 in 1 minute. Thus it must have filled up 5 * 1/12 or 5/12 in 5 minutes. The rest (7/12) was filled by both the pipes jointly. • A + B = 1/12 +1/16 = 28 / 192 or 192/28 minutes are required to fill the tank jointly. • 192/28 *7/12 = 4 minutes. • Thus X is 4 minutes. www.afterschoool.tk
The product of N consecutive positive integers is always divisible by: (1) N! (2) 2n +1 (3) N^2 -1
• We know that product of N consecutive positive numbers can be written as: • N * (N-1) * (N-2) * (N-3) ……... So on. This can be written as N!. Thus answer is (1) .
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A merchant bought 2 varieties of rice costing Rs. 216 & 300 per bag. He mixed them and sold @ 288 per bag after earning 20% profit. What was the ratio of mixture?
• If his cost was 100, selling price was 120. if selling price was 288, cost should be 100/120 *288 =240. • = 60:24 or 5:2 ans.
mixture
216
60
www.afterschoool.tk
240
300
24
If A gives Rs. 20 Lacks to B, A has 40% of what B has. If B gives Rs. 40 Lacks to A, B will have 40% of what A has. What is the amount that A has originally? – 60/80 / 100 • • • • • •
Let us assume that A & B have A & B Rupees. From 1st : .4 (B + 20) = A-20 ; .4B=A -28 From 2nd: .4 (A +40) = B – 40: .4A = B-56: B =.4A + 56 Multiplying 1st equation by 2.5, we get: B = 2.5 A – 70 Deducting this from 2nd equation, we get: 2.1A = 126 A = 126/2.1 = 60 ans.
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2 motorists start at the same time, one from Bikaner to Jaipur and other from Jaipur to Bikaner. If they arrive at destinations in 2 hours and 8 hours respectively after passing each other. How much faster is one driving than other? • The ratio of time (after passing each other) is 2:8 – thus their usual speed is 2:1 (because the faster has already taken that much of advantage as he is running). • Let us take an example, let us take distance of Bikaner to Jaipur as 300 km. Let us assume their speeds to be 20 & 40 they are able to reach mid points at 300/(20+40) = 5hours. First has covered 100 Km and second has covered 200 Km. Now they will have to travel the remaining distances. First will travel 200 /20 and take 10 hours but 2nd will take 100/40 = 2.5 hours, we can find that their ratio is 4:1. www.afterschoool.tk
How many zeroes will be there in X. X = 100! + 200! • Here we have to solve either 100! Or 200! (only one will give the answer – as zeros will not increase by addition). • 100! Is 100*99*98 so on. We know that there are 11 zeroes till 100 directly. We are also able to get additional zero when 5 is multiplied by even number. We have 10 numbers which are ending in 5. out of these, we have one 25, 75 which will give us 2 zeroes. Thus we have 12 zeroes from these. We are able to get one zero from 5 also from 50. thus total we have 11+12+1 = 24 zeroes. Answer.
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The base of a prism is a triangle which has sides 17,25 & 28. the volume of prism is 4200 cubic cm. what is its height? Find its lateral area also?
• Volume of prism = area of base * height • Area of base : hero formulae: • ½ (17+25+28) = 35 area = sqrt (35*18*10*7) = 210 • Height = 4200/210 = 20
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What is the remainder when a prime number greater than 6 is divided by6?
• Either 1 or 5 ans.
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
A clock is set right at 1 pm. It gains 1 min. per hour. What is the true time when the clock shows 6 pm on the same day? • The clock gains 1 minutes per hour – it is faster then the time. Difference of 6 & 1 is 5 hours. We know that when the real difference is 60 minutes, clock shows difference of 61 minutes. Applying the same principle, 60/61 * 300 = 295. 08 that means the real time must be 5.55.08 at that time approx.
www.afterschoool.tk
A vessel weights 16.5 KG when it is full of water. When it is 1/4th full, the weight is 5.25 kg. what is the weight of empty vessel? • Let us assume that weight of vessel is X kg & the material inside weighs Y kg. • X + Y = 16.5 ; X + .25 Y = 5.25; let us multiply 2nd equation with 4. Now it becomes: 4 X + Y = 21 • Deducting 2nd equation from 1st equation, we get: • 3X = 4.5 or X = 1.5 KG. answer. • .
www.afterschoool.tk
In 15 days 9 men and 15 boys can reap a field. In what time could 15 men and 16 boys reap the field assuming 3 men can do as much as 4 boys?
• Convert men into boys. Thus we have 12 + 15 (27) boys doing work in 15 days. • Now we have 20 (15 men are equal to 20 boys) and 16 boys working (total 36 boys). • Applying our trick, solve it as : • 15 * 27 / 36 = 11.25 days.
www.afterschoool.tk
2 taps A & B can fill a tank in 12 & 16 minutes respectively. Both are kept open for X minutes then B is closed. A fills up the rest of tank in 5 minutes. What is X ? • We know that A can fill up 1/12 in 1 minute. Thus it must have filled up 5 * 1/12 or 5/12 in 5 minutes. The rest (7/12) was filled by both the pipes jointly. • A + B = 1/12 +1/16 = 28 / 192 or 192/28 minutes are required to fill the tank jointly. • 192/28 *7/12 = 4 minutes. • Thus X is 4 minutes. www.afterschoool.tk
The product of N consecutive positive integers is always divisible by: (1) N! (2) 2n +1 (3) N^2 -1
• We know that product of N consecutive positive numbers can be written as: • N * (N-1) * (N-2) * (N-3) ……... So on. This can be written as N!. Thus answer is (1) .
www.afterschoool.tk
A merchant bought 2 varieties of rice costing Rs. 216 & 300 per bag. He mixed them and sold @ 288 per bag after earning 20% profit. What was the ratio of mixture?
• If his cost was 100, selling price was 120. if selling price was 288, cost should be 100/120 *288 =240. • = 60:24 or 5:2 ans.
mixture
216
60
www.afterschoool.tk
240
300
24
If A gives Rs. 20 Lacks to B, A has 40% of what B has. If B gives Rs. 40 Lacks to A, B will have 40% of what A has. What is the amount that A has originally? – 60/80 / 100 • • • • • •
Let us assume that A & B have A & B Rupees. From 1st : .4 (B + 20) = A-20 ; .4B=A -28 From 2nd: .4 (A +40) = B – 40: .4A = B-56: B =.4A + 56 Multiplying 1st equation by 2.5, we get: B = 2.5 A – 70 Deducting this from 2nd equation, we get: 2.1A = 126 A = 126/2.1 = 60 ans.
www.afterschoool.tk
2 motorists start at the same time, one from Bikaner to Jaipur and other from Jaipur to Bikaner. If they arrive at destinations in 2 hours and 8 hours respectively after passing each other. How much faster is one driving than other? • The ratio of time (after passing each other) is 2:8 – thus their usual speed is 2:1 (because the faster has already taken that much of advantage as he is running). • Let us take an example, let us take distance of Bikaner to Jaipur as 300 km. Let us assume their speeds to be 20 & 40 they are able to reach mid points at 300/(20+40) = 5hours. First has covered 100 Km and second has covered 200 Km. Now they will have to travel the remaining distances. First will travel 200 /20 and take 10 hours but 2nd will take 100/40 = 2.5 hours, we can find that their ratio is 4:1. www.afterschoool.tk
How many zeroes will be there in X. X = 100! + 200! • Here we have to solve either 100! Or 200! (only one will give the answer – as zeros will not increase by addition). • 100! Is 100*99*98 so on. We know that there are 11 zeroes till 100 directly. We are also able to get additional zero when 5 is multiplied by even number. We have 10 numbers which are ending in 5. out of these, we have one 25, 75 which will give us 2 zeroes. Thus we have 12 zeroes from these. We are able to get one zero from 5 also from 50. thus total we have 11+12+1 = 24 zeroes. Answer.
www.afterschoool.tk
The base of a prism is a triangle which has sides 17,25 & 28. the volume of prism is 4200 cubic cm. what is its height? Find its lateral area also?
• Volume of prism = area of base * height • Area of base : hero formulae: • ½ (17+25+28) = 35 area = sqrt (35*18*10*7) = 210 • Height = 4200/210 = 20
www.afterschoool.tk
What is the remainder when a prime number greater than 6 is divided by6?
• Either 1 or 5 ans.
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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