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# Tutor profile: Arka B.

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Arka B.
Tutor for 9 years in all kind of Maths,Statistics and Business Management
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## Questions

### Subject:Basic Math

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Question:

Richard sold an article to Sam at 25% profit and Sam sold it to Peter at 20% profit. If the article Richard bought at \$600, what is the price at which Peter bought that article?

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Arka B.

We know, Selling Price = Cost Price + Profit Cost Price for Richard is \$600 If he sold it at 25% profit, he has got profit of 25% of \$600 = \$600*25/100 = \$150 Hence Selling price for Richard = Cost Price + Profit = \$600+\$150 = \$750 Now, selling price for Richard is Cost Price for Sam Hence, Cost Price for Sam is \$750 If he sold it at 20% profit, he has got profit of 20% of \$750 = \$750*20/100 = \$150 Hence Selling price for Sam = Cost Price + Profit = \$750+\$150 = \$900 Since selling price for Sam is Cost Price for Peter. Peter has bought the article at \$900

### Subject:Number Theory

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Question:

The product P of two prime numbers are between 59 and 109. If one of them is between 5 and 12 and the other is in between 11 and 21. What is the sum of that 2 prime numbers ?

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Arka B.

The possible prime numbers ( the number which can be divided only by 1 and the number itself) between 5 and 12 are 7 and 11 The possible prime numbers between 11 and 21 are 13,17 and 19 Hence we have two set of prime numbers (7 and 11) and (13, 17 and 19) Below are the possible products 7*13 = 91 7*17 = 119 7*19 = 133 11*13 = 143 11*17 = 187 11*19 = 209 Out of all the possible products only 91 lies between 59 and 109. Hence 7 and 13 are the actual numbers we are looking for. So the sum of the two prime numbers will be 7+13 =20

### Subject:Algebra

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Question:

If |8-a| = 7 and |20-5b| = 10 , what is the minimum value of b/a ?

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Arka B.

We know, modulus of any number means the value of that number can be both positive or negative. For example, modulus of x or |x| = 5 means x can be +5 or -5 Hence in the given question, Equation 1 : |8-a| = 7 Case 1: (8-a) = 7 or a = 8-7 or a = 1 Case 2: (8-a) = -7 or a = 8+7 or a = 15 So from equation 1 , we can get a = 1 or 15 Equation 2 : |20--5b| = 10 Case 1: (20-5b) = 10 or 5b = 20-10 or 5b = 10 or b = 2 Case 2: (20-5b) = -10 or 5b = 20+10 or 5b = 30 or b = 6 So from equation 2 , we can get b = 2 or 6 So b/a can take below 4 values (as both a and b has two values each) 2/1 or 2 6/1 or 6 2/15 or 0.13 6/15 or 0.4 So the minimum value of b/a is 2/15 Alternatively, we can also see if b/a has to be minimum, the numerator or b has to take the least possible value and denominator or a has to take the highest possible value. From the possible values of a and b, b/a can be minimum when b = 2 ( by considering the minimum value between 2 and 6) and a =15 ( by considering the maximum value between 1 and 15) So the minimum value of b/a is 2/15

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