Question

A number of two digits is equal to six times the sum of its digits. If the digits are reversed, the number so formed is equal to

• A. six times the sum of its digits
• B. five times the sum of its digits
• C. ten times the sum of its digits
• D. nine times the sum of digits

Answer 1

The correct option is B five times the sum of its digits

Let the digit be $x$ and $y$
Given, the number of two digits is equal to six times the sum of its digits,

$10x+y=6(x+y)$
$=>10x+y=6x+6y$
$=>4x=5y$
$=>x=\frac{5}{4}y$
Now, when the digits are reversed, the number will be $10y+x$
Let $10y+x=a(x+y)$
$=>10y+\frac{5}{4}y=a(\frac{5}{4}y+y)$
$=>\frac{45}{4}=a\frac{9}{4}$
$=>a=5$
Hence, if the digits are reversed the number so formed is equal to five times the sum of its digits.