For a two digit number, the new two digit number is 47 times of the original number after exchanging the number of its ten digits with the number of its individual digits. What is the original two digit number? How many double digits are there?

For a two digit number, the new two digit number is 47 times of the original number after exchanging the number of its ten digits with the number of its individual digits. What is the original two digit number? How many double digits are there?

Let the original two digits be 10x + y, then the new two digits are 10Y + X, 47 × (10x + y) = 10Y + X & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; 40x + 4Y = 70Y + 7x & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; 33x = 66y & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; X = 2Y; it means that the number of one digit is twice that of ten digit, so y is 1, 2, 3, 4, X can be 2, 4, 6, 8; answer: the original two digit is 21, 42, 63, 84, there are four