Replace star so that 75 star may be divisible by11
Answers
Answer:
Solution :
(i) 39 M 2
The given number = 39 M 2
A number is divisible by 11, if the difference of sum of its digits in odd places from the right side and the sum of its digits in even places from the right side is divisible by 11.
Sum of its digits in odd places = 3 + M
Sum of its digits in even place = 9 + 2 = 11
Their difference :
\Rightarrow11-\left(3-M\right)=0⇒11−(3−M)=0
\Rightarrow11-3-M=0⇒11−3−M=0
\Rightarrow M=8⇒M=8
Therefore, value of M is 8.
(ii) 3 M 422
The given number = 3 M 422
A number is divisible by 11, if the difference of sum of its digits in odd places from the right side and the sum of its digits in even places from the right side is divisible by 11.
Sum of its digits in odd places = 3 + 4 + 2 = 9
Sum of its digits in even places = M + 2
Their difference :
\Rightarrow9-\left(2+M\right)=0⇒9−(2+M)=0
\Rightarrow9-2-M=0⇒9−2−M=0
\Rightarrow M=7⇒M=7
Therefore, value of M is 7.
(iii) 70975 M
THe given number = 70975 M
A number is divisible by 11, if the difference of sum of its digits in odd places from the right side and the sum of its digits in even places from the right side is divisible by 11.
Sum of its digits in odd places = 0 + 7 + M = 7 + M
Sum of its digit in even places = 5 + 9 + 7 = 21
Their difference :
\Rightarrow21-\left(7+M\right)=0⇒21−(7+M)=0
\Rightarrow21-7-M=0⇒21−7−M=0
\Rightarrow M=14⇒M=14
Therefore, value of M is 14.
(iv) 14 M 75
The given number = 14 M 75
A number is divisible by 11, if the difference of sum of its digits in odd places from the right side and the sum of its digits in even places from the right side is divisible by 11.
Sum of its digit in odd places = 1 + M + 5 = M + 6
Sum of its digit in even places = 4 + 7 = 11
Their difference :
\Rightarrow11-\left(6+M\right)=0⇒11−(6+M)=0
\Rightarrow11-6-M=0⇒11−6−M=0
\Rightarrow M=5⇒M=5
Therefore, value of M is 5.