A three-digit number 2 a 3 is added to the number 326 to give a three-digit number 5b9 which is divisible by 9. Find the value of b - a.
Solution:
2a3 is added to 326 as shown below and the resultant number 5b9 is divisible by 9.
2 a 3
+3 2 6
5 b 9
If 5b9 is divisible by 9 then the sum of its digits should be divisible by 9.
5 + b + 9 = 14 + b is divisible by 9
For 14 + b to be divisible by 9 the minimum value of b = 4. The other values of
are b = 13, 22….. But since b is single digit these values of b are invalid.
b = 4 and therefore
b = a + 2 = 4
a =2
b - a = 4 - 2 = 2
✦ Try This: A three-digit number 3 a 4 is added to the number 437 to give a three-digit
number 8b1 which is divisible by 9. Find the value of a - b.
3 a 4
+4 3 7
8 b 1
Looking at the units place of both the three digit numbers being added we have,
4 + 7 = 11 (1 remains in the units place and 1 carries over)
Looking at the ten’s place we have
a + 1 + 3 = b
Since 7b1 is divisible by 9 then
7 + b + 1 is divisible by 9
Minimum value of b is 1 because 7+ 1 + 1 = 9 is divisible by 9
The next value of b is 10 but that is not valid because it is two digit.
Now if b = 1 then
1(from carry over) + a + 3 = 11 (1 will carry over to hundreds place)
a = 11 - 1 - 3
a = 7
a - b = 7 - 1 = 6
☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 16
NCERT Exemplar Class 8 Maths Chapter 13 Problem 66
A three-digit number 2 a 3 is added to the number 326 to give a three-digit number 5b9 which is divisible by 9. Find the value of b - a.
Summary:
A three-digit number 2 a 3 is added to the number 326 to give a three-digit number 5b9 which is divisible by 9, the value of b - a is 2.
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