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 :
A. k - 1
B. 11 - k
C. 9 + k
D. 10 - k
Answer: Option B
Solution(By Examveda Team)
Let the ten's digit be x and the unit's digit be yThen, number = 10x + y
$$\eqalign{ & \therefore 10x + y = k\left( {x + y} \right) \cr & \Rightarrow k = \frac{{10x + y}}{{x + y}} \cr} $$
Number formed by interchanging the digits = 10y + x
Let, 10y + x = h(x + y)
Then,
$$\eqalign{ & h = \frac{{10y + x}}{{x + y}} \cr & \,\,\,\,\, = \frac{{11\left( {x + y} \right) - \left( {10x + y} \right)}}{{x + y}} \cr & \,\,\,\,\, = 11 - \frac{{10x + y}}{{x + y}} \cr & \,\,\,\,\, = 11 - k \cr} $$
Related Questions on Problems on Numbers
If one-third of one-fourth of a number is 15, then three-tenth of that number is:
A. 35
B. 36
C. 45
D. 54
E. None of these
A. 9
B. 11
C. 13
D. 15
E. None of these
A. 3
B. 4
C. 9
D. Cannot be determined
E. None of these
Join The Discussion