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InterviewSolution
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Divide 32 into two parts such that their product is 175? |
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Answer» Let the four parts be (a - 3d), (a - d), (a + d) and (a + 3d). Then,Sum of the numbers = 32 {tex}\\Rightarrow{/tex}(a - 3d) + (a - d) + (a + d) + (a + 3d) = 32\xa0{tex}\\Rightarrow{/tex} 4a = 32\xa0{tex}\\Rightarrow{/tex} a = 8It is given that{tex}\\frac { ( a - 3 d ) ( a + 3 d ) } { ( a - d ) ( a + d ) } = \\frac { 7 } { 15 }{/tex}{tex}\\Rightarrow \\quad \\frac { a ^ { 2 } - 9 d ^ { 2 } } { a ^ { 2 } - d ^ { 2 } } = \\frac { 7 } { 15 }{/tex}{tex}\\Rightarrow \\quad \\frac { 64 - 9 d ^ { 2 } } { 64 - d ^ { 2 } } = \\frac { 7 } { 15 } \\Rightarrow{/tex}128d2 = 512\xa0{tex}\\Rightarrow{/tex} d2 = 4\xa0{tex}\\Rightarrow{/tex}d = ± 2Thus, the four parts are a - 3d, a - d, a + d and a + 3d i.e., 2,6,10,14. 25 and 7 its product = 175 But it said to divide it into two parts... |
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