$A 3 - d i g i t$ number $4 A 3$ is added to another $3 - d i g i t$ number $984$ to give four digit number $13 B 7$ , which is divisible by $11$ . Find $(A + B)$

Open in App

Solution

$4 A 3 + 984 = 13 B 7$
We can observe that $A$ and $B$ are single digits .so, they must lie between $[0, 9]$
Now, since it is divisible by $11$ it must follow divisibility rule of $11$
which is, The alternative sum of the digits of Number is divisible by $11$
$\Rightarrow 1 - 3 + B - 7$ is to be divisible by $11$ or $1 - 3 + B - 7 = 11 α$
Also, $13 B 7$ can also be written as $11 α$ where $α$ is any integer
here, since $B$ can only lie between $[0, 9]$ , only value of $α$ satisfying $1 - 3 + B - 7 = 11 α$ is $0$
$\Rightarrow 1 - 3 + B - 7 = 0 \Rightarrow B = 9$
Also, $B = A + 8 \Rightarrow 9 = A + 8 \Rightarrow A = 1$
Therefore, $A = 1, B = 9$
So. $A + B = 10$

Suggest Corrections

Similar questions

Q. If a

3

digit numbers

4 a 3

is added to another

3

digit number

984

to give four digit number

13 b 7

and it is visible by

11,

then

a + b = ?

Q. Q. A 3-digit number 4a3 is added to another 3-digit number 984 to give the four-digit number 13b7, which is divisible by 11. Then (a + b) is

Question 66

A three-digits number 2a3 is added to the number 326 to give a three-digits number 5b9 which is divisible by9. Find the value of b - a.

Four digit numbers are formed using the digits $1, 2, 3, 4$ (repetitions among the digits allowed). Find the number of such four digit numbers divisible by $11$

Q. The three-digit number 2a3 is added to the number 326 to give the three-digit number 5b9. If 5b9 is divisible by 9, then

a + b

equals

Join BYJU'S Learning Program

A 3−digit number 4A3 is added to another 3−digit number 984 to give four digit number 13B7, which is divisible by 11. Find (A+B)

$A 3 - d i g i t$ number $4 A 3$ is added to another $3 - d i g i t$ number $984$ to give four digit number $13 B 7$ , which is divisible by $11$ . Find $(A + B)$