If a two digit no. is" k" times the sum of its digits and the no. formed by interchanging it's digits is" m" times the sum of the digits then "m"is equal to
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a two digit number is "k" times the sum of it's digits, 10x + y = k(x+y)
same two digit number are interchanged is "m" times the sum of it's digits, 10y + x = m(x+k)
sum both equations,
10x + y + 10y + x = k(x+y) + m(x+y)
11x + 11y = (k + m)(x + y)
11(x + y) = (k + m)(x + y)
k + m = 11
so m = 11 - k
same two digit number are interchanged is "m" times the sum of it's digits, 10y + x = m(x+k)
sum both equations,
10x + y + 10y + x = k(x+y) + m(x+y)
11x + 11y = (k + m)(x + y)
11(x + y) = (k + m)(x + y)
k + m = 11
so m = 11 - k
sibhiamar:
no problem
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