What 4 digit number multiplied by 9 is itself backwards?
Answers
For 4-digit numbers, let a, b, c, and d be the digits, so
9*(1000*a+100*b+10*c+d) = 1000*d + 100*c + 10*b + a
8999*a + 890*b = 10*c + 991*d
This implies that d = 10 - a, by looking at last digits, which we
substitute, and get
9990*a + 890*b = 10*c + 9910
When we divide by 10, we get
999*a + 89*b = c + 991
This implies that a = 1, so
89*b = c - 8
This implies that b = 0 and c = 8, and there is only one solution
9*1089 = 9801.
Given : a 4 digit number is multiplied by 9 its digits get reversed.
To Find : the 4 digit number.
Solution:
ABCD * 9 = DCBA
A must be 1 as greater than 1 multiplied by 9 will result in 5 digit number
1BCD * 9 = DCB1
D must be 9 as only 9 * 9 = 81
=> 1 BC9 * 9 = 9CB1
C * 9 + 8 = 10X + B X is carry over
B * 9 + X = C and no carry over as 1* 9 = 9 in last
so B must be 0
=> X = C
C * 9 + 8 = 10C + 0
=> C= 8
1089 * 9 = 9,801
1089 is 4 digit number
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