The number 4ab5 is divisible by 55 then what is the value of b-a
Answers
Answer:
Step-by-step explanation:
55=5*11.
We know in the no. 4ab5 last digit is 5 so its divisible by 5.
Its divisible by 11 also if its divisible by 11 then the sum of its odd and even terms must be divisible by
11.
4+b-(a+5)=a no. Divisible by 11.
b-a=(a no. Divisible by 11 ) +1.
now since b and a are single digit no. so 0 is the only no. which satisfies the equation. So the answer is 1.
Given:
4ab5 is divisible by 55.
To Find:
The value of b-a.
Solution:
1) If a number is divisible by 55 then the number must be divisible by 5 and 11 both.
2) The divisibility rule for 5 is that the unit digit must be 0 or 5.
3) The divisibility rule for 11 is that the difference of the sum of the alternative digits of the given number must be 0 or any factor of 11.
4) 4ab5 is divisible by 5 as it is clearly mentioned that the unit digit is 5.
5) If 4ab5 is divisible by the 11 it must follow the divisibility of 11.
(4+b)-(a+5) = 0 or 11
6) If (4+b)-(a+5) = 0
- b-a-1 = 0
- b-a = 1
7) If (4+b)-(a+5) = 11
- b-a-1 = 11
- b-a = 12