3 June Maths I

MATHS Dr. T.K. Jain. AFTERSCHOOOL M: 9414430763 [email protected] www.afterschool.tk www.afterschoool.tk

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The population of a town is 100000, what was it two years back, if it has been growing @10%? • The process is to divide this number by 1.1*1.1. Remember, in order to get the population 2 years after, we will multiply it by 1.1*1.1 and in order to get the population two years back, we will divide it by 1.1*1.1. Re. 1 of today will become 1.1 after one year – so logically we have to divide it by 1.1. • =100000/1.1*1.1 = 82644 Ans. www.afterschoool.tk

The population of a town is 100000, what will it be two years after, if it has been growing @10%?

• =100000*1.1*1.1 • =121000 • Ans.

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What is the present worth of Rs. 5000 due 3 years hence? R = 10%

• • • • •

Formulae of present worth is : =100*amt/(100+(r*t)) =100*5000/(100+(10*3) 500000/130 =3846 Ans.

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How much money will bank give you, if you if you take your bill to the bank for discounting. The bank charges@10%. The due date of bill is 3 years hence. What will be gain of Bank? • Bankers’ discount: 5000*10%*3= 1500 • To get banker’s gain, find the difference of bankers discount and true discount. • True discount = Amt – Present worth • =5000-3846= 1154 • Banker’s gain= 1500-1154 = 346 Ans. www.afterschoool.tk

How should I mix rice costing 31 per kg with rice costing 36 per kg so that my net costing becomes 32.5 only? MIXTURE

31

32.5

3.5

36

1.5

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I want to sell wheat @ 50/- per kg after earning 25% profit. I have two varieties, one costing Rs. 33 & II costing Rs. 48. How should I mix them? • My price is 50, but profit is 25% on cost. Thus cost is : 50*100/125 = 40 • Now I have to find the mixture, which can give me cost of 40. • The first variety costs 33 & II costs 48 and target is 40. • The answer is 8:7 .. See the next slide.

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In what ratio must a person mix rice costing 120, 144 &174, so that the final cost is 141 per kg.? • The target cost is 141. we have to compare two cost structures at a time and find their ratio and then find their combined ratio. • We cant compare 144 & 174 – because both are above the target cost. We will take those values – which are one above target, one below target. Therefore we will compare 120 & 144 in the first time and 120&174 next time. www.afterschoool.tk

Solution:1 MIXTURE

120 3

141

144 21

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Solution - 2 MIXTURE

120 33

141

174 21

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Solution -- 3 First ratio is : 3:21 Second ratio is 33:21 3 is common in all these, so divide by 3: I: 1:7; II: 11:7. the first item is common in these, so the first values are multiplied with the second values of each other – to get combined ratio: • 11:77:7 Ans. • • • •

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Solution … mixture

33

48

40 8

7

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SOLUTION … • The rice costing 31 and 36 should be mixed in the ratio: 3.5:1.5 or • Or 7:3 • i.e. if we want to make a mixture of 10 kg, we will take 7 kg. of rice costing 31 and 3 kg of rice costing 36.

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If A:B = 2:3, B:C=4:5, what is a:b:c? • A:B = 2:3, B :C= 4:5 • • Here common element is B, so put b over b. multiply elements of b with each other : 3*4 = 12. Now cross multiply B of second with A of first; and B of first with C of second: • 2*4 and 3*5. We get new ratio of A & C as :10 and 15. • The new ratio of A:B:C = 8:12:15 Ans. • Remember, we have to multiply other elements with common elements. If we multiply B&C with each other, answer will be something different. www.afterschoool.tk

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

• A:B = 2:3, • A: C=4: 5 • Put A beneath A. multiply both the values of A: 2*4= 8 this is the A. • Cross multiply first A with second C and will you get C = 2*5 = 10 • Cross multiply second A with first B, you get B = 4*3 = 12 • Ratio of A:B:C = 8:12:10 ans. www.afterschoool.tk

What is the ratio of B:C, if A:B = 5:12, A:C=11:13?

• We know that : • B/A * A/C = B/C (A gets cancelled) • Therefore convert first ratio (A:B) into B:A; It is 12:5. (A= 5 & B = 12, put it reverse order) • We cant solve it by A/B – Because, A/B & A/C will not give us B/C. • Now 12/5 *11/13 = 12*11 / 5*13 • =132 / 65 Ans. www.afterschoool.tk

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