1 July Mathematics Ratio

Mathematics – Ratio Dr. T.K. Jain. AFTERSCHOOOL Centre for social entrepreneurship Bikaner M: 9414430763 [email protected] www.afterschoool.tk www.afterschool.tk

Inverse ratio of 11:15? • 15:11

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Ratio of two quantities is 4:5. the antecedent is 24, what is consequent? • Divide 24 by 4, we get 6. • Multiply 6 by 5, we get 30. this is answer. • Antecedent is the number coming first and consequent is the number coming second in the ratio. Quantitities are : 24:30. answer. www.afterschoool.tk

Duplicate ratio of 3:4? • Square these numbers: • 9:16

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Triplicate ratio of 2:3? • Cube of these: • 8:27

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Angles of a traingle are in the ratio of 4:5:9. what are the angles. • We know that sum of angles in a triangle is 180 degree. • Total 4:5:9 = 18. • First angle is 4/18 *180 = 40 • 2nd angle = 5/18 *180 = 50 • 3rd angle is = 9/18 *180 = 90 answers.

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Angles of a quadrilateral are in the ratio of 3:4:5:6. what are the angles.

• We know that sum of angles in a triangle is 360 degree. • Total 3,4,5,6 = 18. • First angle is 3/18 *360 = 60 • 2nd angle = 4/18 *360 = 80 • 3rd angle is = 5/18 *360 = 100 • 4th angle is 6/18 * 360 = 120 answers. www.afterschoool.tk

A & B have earning in ratio of 4:5 and expenses in ratio 7:9. Each saves Rs. 50. what is their income? • • • •

Let us assume incomes to be 4x & 5 y. Let us assume expenses to be 7y &9y. saving= income – expenses. 4x-7y = 50 and 5x-9y = 50 multiply 1st equation by 9 & 2nd equation by 7 and then subtract from each other. • 36x-63y=450 and 35y-63y=350 • X = 100. Thus incomes of A & B are 400 & 500 answer. . www.afterschoool.tk

Divide 324 between A & B in ratio 11:7. ? • Sum up 11 & 7 = 18. • A’s share: 11/18 *324 = 198 • B’s share = 324-198 = 126

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A:B = 2:3, B:C = 3:5, what is a:b:c? • • • • •

Put these figures as under: A:B:C 2:3 3:5 Now take B as common – which is 3. Since in both the cases B’s value is 3, so combined ratio is 2:3:5. answer. www.afterschoool.tk

A:B = 2:3, B: C = 4:5, what is a:b:c? • • • • •

Put these figures as under: A:B:C 2:3 4:5 Now take B as common – which is 3&4. We have to get same value of B. multiply 4 to both the upper numbers and multiply 3 to both the lower numbers. Now B’s value is same in both – 12. Now ratio is : 8:12:15. www.afterschoool.tk

12:16:x:20 are in proportion, what is X? • Step 1: multiply 1st and 4th term and multiply 2nd and 3rd term. 2st * 4th = 2nd * 3rd. (in proportion, product of 1st and 4th is equal to product of 2nd and 3rd) 240 = 16x X = 15 answer. www.afterschoool.tk

2 numbers are in ratio of 3:4 and if 6 is added to them, the new ratio is 4:5. What are the numbers? • • • • •

Let us assume numbers to be 3x & 4x. 3x+6 / 4x+6 = 4/5 15x+30 = 16x + 24 -x =-6 X = 6 answer.

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x/2 = y/3 = z/7, what is value of (2x3y+4z)/3y • Let us assume value of X =2, y = 3 and z=7. • Put these values and get the answer. • (4 -9+28) / 9 • = 23/9 answer .

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What is invertendo? • • • •

P:q:: a:b Is also: q:p ::b:a (reverse the ratio).

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What is alternendo? • If a:b = e:f • Then we can write as a:e = b:f • (taking alternate values and preparing ratio from them).

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What is componendo? • • • •

If a:b = e:f We can also write: A+b:b = e+f :f (combining the 2 numbers and taking ratio with one of the components)

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What is Dividendo? • • • •

If a:b = e:f We can also write: A-b:b = e-f :f (dividing the 2 numbers and taking ratio with one of the numbers)

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What is addendo? • • • •

If a:b = e:f We can also write as: A+E: B+F (HERE WE ADD FIRST TERMS AND SECOND TERMS).

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WHAT IS COMPONENDO & DIVIDENDO? • IF A:B = E:F • WE CAN WRITE AS: • A+B: A-B = E+F: E-F

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WHAT IS SUBTRAHENDO? • • • •

If A:B = E:F We can write as: A-E : B-F (subtract first term from first and 2nd term from 2nd).

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What is mean proportion between 2kg and 8 kg. • To get mean proportion, we have to get geometric mean out of these: • Multiply 2 & 8 = 16 • Now take square root of 16 = we get 4 this is answer.

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4, X, 9, 13.5 are in proportion. What is X? • Multiply 1st and 4th term = it will be equal to multiply of 2nd and 3rd term. • 4*13.5 = x*9 • 9X = 54 • X = 6 answer.

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(5x-3y) / (5y – 3x) = ¾, what is value of X & Y? • Let us assume : 5x-3y = 3 • Let us assume : 5y-3x = 4 (write as 3x-5y=-4) • Now multiply firs equation with 3 & 2nd equation by 5. we get: 15x-9y=9 and 15x-25y=-20) (or -15x+25y = 20) • Subtract 2nd equation from 1st equation: • 16y = 29. Y = 29/16 = 1.8125 • Now put the value of Y in any equation and get the value of X. 5x – 3*1.8125 = 3 • 5x =3+5.44 • X = 8.44/5 X = 1.688 answer. www.afterschoool.tk

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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)

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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.

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