# Sol if we denote the date of birth by d and the month

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1.03.Lokesh bought two varieties of books – A and B. Each book of variety. A cost `30 and each book of variety B cost `40. He spent a total of `720 for purchasing these books. How many different combinations are possible for his purchase?
1.04.Rohit bought bars of two varieties of ice cream. The first variety cost `9 per bar. The second variety cost `11 per bar. He paid a total of `227 for his purchase. How many different combinations are possible for his purchase? Sol: Let the numbers of the first variety and second variety of ice cream bars she bought be x and y respectively. 9x +11y = 227 dividing both sides by 9, x +911y = 25 +992y11-= 25 -Let 25 -x = k (1) k is an integer. y =112k9+
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Triumphant Institute of Management Education Pvt. Ltd.(T.I.M.E.) HO:95B, 2ndFloor, Siddamsetty Complex, Secunderabad – 500 003.y is an integer. 9k +2 must be divisible by 11. k can be 1, 12, 23, 34,…… If k > 23, x < 0 k has 3 possibilities (x, y) has 3 possibilities. 1.05.13x -11y = 43 where x is a positive integer. Find the number of possible values of (x, y), if 16 < x < 40. Sol: Given 13x – 11y = 43 Dividing both sides by 11, x +112x -y = 3 +11-x +y +3 =1110x2Let y +3 -x = k k is an integer. x =211210k11=+k +5 (1) 16 <211k +5 < 40. 2 < k < 1170= 6114To satisfy (1), k must be even. k has 2 possibilities. x has 2 possibilities. Alternate solution: 13x – 11y = 43 We first find one solution. The other solutions can be obtained by successively adding 11 to the value of x and adding 13 to the value of y. We see that Rem1143= 10 and Rem-11y11x13= Rem11x13. As Rem11x13= 2, x = 5 satisfies the equation. Different values of x, y that satisfy the equation are listed below. 13 (5) – 11 (2) = 43 13 (16) – 11 (15) = 43 and 13 (27) – 11 (28)= 43 and 13 (38) – 11 (41) = 43 There are two values of x such 16 < x < 40, that satisfy the equation.
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