InterviewSolution
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InterviewSolution
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(iv) The sum of the digits of a number consistingof three digits is 12, The middle digit is equalto half the sum of the other two. If the orderof the digits is reversed, the number isdiminished by 198. Find the number. |
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Answer» Let a, b, c = the three digitsthen100a+10b+c = "the number":Write an equation for each statement simplify as much as possible::the sum of the digits of a number consisting of three digit is 12.a + b + c = 12:he middle digit is equal to half of the sum of the other two.b = .5(a+c):if the order of the digit be reversed the number is diminished by 198 find be number100c + 10b + a = 100a + 10b + c - 198100c - c + 10b - 10b = 100a - a - 19899c = 99a - 198simplify, divide by 99c = a - 2: In the 2nd equation, b = .5(a+c), replace c with (a-2)b = .5(a + a - 2)b = .5(2a-2)b = a - 1:In the 1st equation replace b with (a-1); replace c with (a-2)a + (a-1) + (a-2) = 123a - 3 = 123a = 12 + 3a = 15/3a = 5then using the above equations we know that:b = 4andc = 3:543 is the number b= 5(2a-2) kaise kiyab= a-1 |
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