Question

please help me know plz I had a lot of confusion u know ​

Answer 1

Given :

★  The first three digit number is 4A3

★  The second three digit number is 984

★  When 4A3 and 984 are added, Result is a four digit number 13B7

We can notice that :

★  Digits in the unit's place of three digit numbers are 3 and 4

★  When digits in the unit place of these three digit numbers are added, we get (3 + 4) = 7 as the digit in the unit's place of four digit number

★  Digits in the hundred's place of three digit numbers are 4 and 9

★  When digits in the hundred's place of these three digit numbers are added, we get (4 + 9) = 13

★  The digits in the hundred's place and thousand's place of four digit number (13B7) are 3 and 1 respectively, which are the same digits we got when digits in the hundred's place of three digit numbers are added. It conforms us that the sum of the digits in the ten's place of three digit numbers does not exceed 9

★  Digits in the ten's place of three digit numbers are A and 8 and their sum is (A + 8). The digit in ten's place of four digit number (13B7) is B. As the sum of the digits in the ten's place of three digit numbers does not exceed 9, the sum (A + 8) should be equal to B ⇒ (A + 8) = B

$\implies \begin{tabular}{|c|c|c|}\cline{1-3} \sf{4} & \sf{A} & \sf{3}\\\cline{1-3} \sf{9} & \sf{8} & \sf{4}\\\cline{1-3}\sf{9 + 4} & \sf{A + 8} & \sf{3 + 4}\\\cline{1-3} \sf{13} & \sf{A + 8} & \sf{7}\\\cline{1-3} \sf{13} & \sf{B} & \sf{7}\\\cline{1-3}\end{tabular}\\\\\\\mathsf{\implies A + 8 = B}$

Given : Four digit number (13B7) is divisible by 11

Divisibility criterion for a number to be divisible by 11 :

★  A number is said to be divisible by 11, if the difference between the sum of its digits in the odd places and the sum of its digits in the even places is either zero or a number divisible by 11

As the number 13B7 is divisible by 11, the difference between the sum of its digits in the odd places and the sum of its digits in the even places should be equal to zero (as we concluded that B is a single digit number)

★  The digits in the odd places of 13B7 are 7 and 3

★  Sum of the digits in the odd places of 13B7 = (7 + 3) = 10

★  The digits in the even places of 13B7 are B and 1

★  Sum of the digits in the even places of 13B7 = (B + 1)

$:\implies$  10 - (B + 1) = 0

$:\implies$  10 - B - 1 = 0

$:\implies$  B = 9

Substituting value of B in A + 8 = B, We get :

$:\implies$  A + 8 = 9

$:\implies$  A = 1

$:\implies$  The Value of (A + B) = (9 + 1) = 10