M = abc is a three digit number and N = cba, if M > N and M - N + 396c = 990. Then how many values of M are more than 300.
Correct answer: A
Explanation
From the given data,
abc – cba + 396c = 990
100a + 10b + c – (100c + 10b + a) + 396c = 990
99a – 99c + 396c = 990
Observe that each term is divisible by 99. So on dividing the above expression by 99, we get
a – c + 4c = 10
a + 3c = 10
For c = 1, a = 7
c = 2, a = 4
c = 3, a = 1
'b' can take any value from 0 to 9
We have to find the value of M more than 300. So minimum value of 'a' should be 4.
So total possibilities are 402, 412, ...., 492 = 10 values
701, 711, ....., 791 = 10 values
So total values = 20.
Correct option: A
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