9 Views

Question : If a certain number of two digits is divided by the sum of its digits, the quotient is 6 and the remainder is 3. If the digits are reversed and the resulting number is divided by the sum of the digits, the quotient is 4 and the remainder is 9. The sum of the digits of the number is:

Option 1: 6

Option 2: 9

Option 3: 12

Option 4: 4


Team Careers360 8th Jan, 2024
Answer (1)
Team Careers360 11th Jan, 2024

Correct Answer: 12


Solution : Let the number be $10x + y$.
Dividend = Divisor × Quotient + Remainder
$10x + y = 6(x + y) + 3$
⇒ $10x + y = 6x + 6y + 3$
⇒ $10x – 6x + y – 6y = 3$
⇒ $4x – 5y = 3$ (equation 1)
After interchanging the digits, we have:
$10y + x = 4 (x + y) + 9$
⇒ $10y + x = 4x + 4y + 9$
⇒ $6y – 3x = 9$
⇒ $2y – x = 3$ (equation 2)
From equation 1 and 2, we get:
$4x – 5y = 3$
$2y – x = 3$ (multiplying by 4)
Solving the equation, we get $y = 5$.
Putting the value of $y$ in equation (2),
$2×5 – x = 3$
⇒ $x = 10 – 3 = 7$
So, the sum of digits = $(x + y)=7 + 5 =12$
Hence, the correct answer is 12.

SSC CGL Complete Guide

Candidates can download this ebook to know all about SSC CGL.

Download EBook

Know More About

Related Questions

TOEFL ® Registrations 2024
Apply
Accepted by more than 11,000 universities in over 150 countries worldwide
Manipal Online M.Com Admissions
Apply
Apply for Online M.Com from Manipal University
View All Application Forms

Download the Careers360 App on your Android phone

Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile

150M+ Students
30,000+ Colleges
500+ Exams
1500+ E-books