Question : Two positive numbers differ by 3951. When the larger number is divided by the smaller number, the quotient is 12 and the remainder is 13. The sum of the digits of the larger number is:
Option 1: 12
Option 2: 16
Option 3: 18
Option 4: 14
Correct Answer: 16
Solution :
Let the bigger number be $x$ and the smaller number be $y$.
Given that $x-y=3951$-----------------(1)
Also, According to the question,
$x=y×12+13$
$⇒x-12y=13$-----------------------(2)
Subtracting equation (2) from equation (1), we get,
$11y=3938$
⇒ $y = 358$
So, $x=3951+358=4309$
$\therefore$ The sum of the digits of the larger number = 4 + 3 + 0 + 9 = 16
Hence, the correct answer is 16.
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