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Lecture 06
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Basics of Proportions

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1. RATIO & PROPORTIONS Lecture 06 Venkatesan S IIMB Alumni

2. Trick 1: a+c+e e+c -=-=-= = b d f b+d+f b+d 1 341+3 4 2 6 8 2+6 8

3. Given that a, b and c are in continued proportion; b, c and d are also in continued proportion; and c, d and e are also in continued proportion. If b:c 3:4 and all the five numbers are positive integers, what is the minimum possible value of (a + b+e)? 1. 444 2. 445 3. 592 4. Cannot be determined

4. Given that a, b and c are in continued proportion; b, c and d are also in continued proportion; and c, d and e are also in continued proportion. If b:c 3:4 and all the five numbers are positive integers, what is the minimum possible value of (a +b+e)? a:b: b:c; b:c c:dc:d:: d:e 1. 444 2. 445 3. 592 4. Cannot be determined D2 ce

5. Given that a, b and c are in continued proportion; b, c and d are also in continued proportion; and c, d and e are also in continued proportion. If b:c 3:4 and all the five numbers are positive integers, what is the minimum possible value of (a +b+e)? a:b: b:cb:c: c:dc:d: d:e B2 =a * c => 9x2 = a * 4 => a = 9x2 / 4 1. 444 2. 445 3. 592 4. Cannot be determined D2 = c * e => 256x4 / 9 = 4*e => e = 64x4 / 9

6. Given that a, b and c are in continued proportion; b, c and d are also in continued proportion; and c, d and e are also in continued proportion. If b:c 3:4 and all the five numbers are positive integers, what is the minimum possible value of (a b e)? 1. 444 2. 445 3. 592 4. Cannot be determined B2=a*c=> 9x: = a * 4 => a =3x2 / 4 C2 = b *d => 16x2-d * 3 => d = 16x2 / 3 D2 ce > 256x4 /9 4*ee 64x4 /9 9x2 4 3x 9 /4 81 16x/3 64x4/9 16/3 64/9 192 4 108 144 256

7. Given that a, b and c are in continued proportion; b, c and d are also in continued proportion; and c, d and e are also in continued proportion. If b:c 3:4 and all the five numbers are positive integers, what is the minimum possible value of (a b e)? 1. 444 2. 445 3. 592 4. Cannot be determined C2 b*d> 16x2-d 3 d 16x2/3 D2 ce > 256x4 /9 4*ee 64x4 /9 9x2 4 3x 9 /4 81 16x/3 64x4/9 16/3 64/9 192 a+b+e 81 108256 445 4 108 144 256

8. Variations Gives the interdependency between variables. i.e., how the change of value in one variable affects other.

9. Variations Distance covered Speed , time constant Distance covered ox time,speed constant Speed X time, distance-constant

10. Example Volume varies inversely with Pressure while Volume varies directly with Temperature., Whern volume = 50 m3 . Temperature = 25 C; Pressure = 1 atm. If Volume becomes 300m3 and pressure is constant, find the temperature. 1. 100 C 2. 50 C 3. 125 C 4. 150 C

11. The cost of a diamond varies directly with the cube of its weight. A diamond merchant accidentally dropped a diamond and it broke into four pieces with the weights of the ratio being 1:2:3:4. When the pieces were sold individually, the merchant got Rs.9,00,000 less as compared to what he would have got had he sold the original diamond. Find the price of the original diamond 1. Rs. 10 lakhs 2. Rs. 15 lakhs 3. Rs. 20 lakhs 4. Rs. 25 lakhs

12. The cost of a diamond varies directly with the cube of its weight. A diamond merchant accidentally dropped a diamond and it broke into four pieces with the weights of the ratio being 1:2:3:4. When the pieces were sold individually, the merchant got Rs.9,00,000 less as compared to what he would have got had he sold the original diamond. Find the price of the original diamond 1. Rs. 10 lakhs 2. Rs. 15 lakhs 3. Rs. 20 lakhs 4. Rs. 25 lakhs No loss in weight. x3 + 2x3 + 3x3 + 4x3 = 1 + 8 + 27 + 64 = 100x3 10x3 = 1000x3 Diff in prices = 1000x3-100x3 900x3 9,00,000 Original Weight 1000x310,00,000