Quantitative Aptitude Ques 1237

Question: If a number of two digits is k times the sum of its digits, then the number formed by interchanging the digits is the sum of the digits multiplied by [GIC (AAO) 2011]

Options:

A) $ 9+k $

B) $ 10+k $

C) $ 11-k $

D) $ k-1 $

E) None of these

Show Answer

Answer:

Correct Answer: C

Solution:

  • Let the number be $ 10x+y. $ Then, $ 10x+y=k(x+y) $ …(i) Now, by interchanging the digits, we get the number $ 10+x. $ Now, $ 10y+x=11y+11x-10x-y $ $ =11(x+y)-k(x+y) $ [from Eq. (i)] $ =(11-k)(x+y) $

$ \therefore $ Number is $ (11-k). $

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