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:
a) 12
b) 16
c) 18
d) 20
Sol:
Two positive numbers differ by 3951
When larger number is divided by the smaller number ,
Quotient is 12 and the remainder is 13
Formula Used:
Dividend = Divisor × Quotient + Remainder
Calculation:
Let us assume the larger number be x and the smaller number be y
⇒ x – y = 3951 ………….(1)
According to the given question, when larger number is divided by smaller number,
quotient = 12, remainder = 13
⇒ Dividend = Divisor × Quotient + Remainder
⇒ x = y × 12 + 13 ⇒ x – 12y = 13 ………..(2)
On subtracting eq( 1 ) – eq (2),we get
⇒ 11y = 3938
⇒ y = 358
Now, put the value of y in eq(1), we get
⇒ x – 358 = 3951
⇒ x = 3951 + 358 = 4309
Sum of the digits of the larger number x = 4 + 3 + 0 + 9 = 16 Hence, sum of the digits of the larger number is 16.
