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Lecture 07
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Variations

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thanku sir
1. RATIO & PROPORTIONS Lecture 07 Venkatesan S IIMB Alumni

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

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

4. 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

5. 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

6. 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

7. 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

8. 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

9. The price of Assam tea (in rupees per kilogram) is 100+ 0.1n on the nth day of 2011 (for n 1,2,..100) and then remains constant. On the other hand the price of Shillong tea (in rupees per kilogram) is 89 0.15n on the nth day of 2011 (n 1,2,.365). On which date in 2011 the prices of both varieties of tea will be equal 1. May 20 2. May 21 3. Aug 8 4. Aug 9

10. The price of Assam tea (in rupees per kilogram) is 100+ 0.1n on the nth day of 2011 (for n 1,2,..100) and then remains constant. On the other hand the price of Shillong tea (in rupees per kilogram) is 89 0.15n on the nth day of 2011 (n 1,2,.365). On which date in 2011 the prices of both varieties of tea will be equal 1. May 20 Shillong 89+ 0.15n Assam 100+0.1 n 2. May 21 3. Aug 8 100 +0.1n89+0.15n 0.05n 11 n 11/0.05 4. Aug 9 n 220

11. So, the general form of such variations will be, A K1+K2 B