Two positive numbers differ by 3951. When the larger number is divided by the smaller number, the quotient is 12

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.