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The sum of two numbers is 16 and the sum of their reciprocals isFind the numbers.(CBSE 2005]There are two classrooms A and B. If 10 students are sent from A to B,the number of students in each room becomes the same. If 20 studentsare sent from B to A, the number of students in A becomes double thenumber of students in B. Find the number of students in each room. |
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Answer» Let one number be x.other number = 16 - x(because sum of two numbers is 16)A/Q 1/x + 1/(16 - x) = 1/3 16 -x +x / x(16 -x) = 1/3 16*3 = x(16 - x) 48 = 16x - x² x² - 16x + 48 = 0 x² - 12x - 4x + 48 =0x(x-12) -4(x-12) =0 x-4 = 0 or x-12 =0 x=4 or x=12hence one Number is 4 .and another number = 16 - x =16 - 4 =12. Let the number of students in classroom A be x and the number of students in classroom B be y. If 10 students are transferred from A to B, then we have: x – 10 = y + 10 x – y = 20 …..(i) If 20 students are transferred from B to A, then we have: 2(y – 20) = x + 202y – 40 = x + 20 -x + 2y = 60 …..(ii) On adding (i) and (ii), we get: y = (20 + 60) = 80On substituting y = 80 in (i), we get: x – 80 = 20 x = (20 + 80) = 100 Hence, the number of students in classroom A is 100 and the number of students in classroom B is 80. |
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