# In a two digit number, the digit in the ten's place is 3 more than the digit in the one's place. 7 times the sum of the digits is 3 more than the number. find the number

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74 is the number as 7 is 3 more than 4

7+4=11

11 x 7=77

so 74+3=77

hence the answer is 74

7+4=11

11 x 7=77

so 74+3=77

hence the answer is 74

A = B + 3

7(A + B) = 3 + AB

7(B + B + 3) = 3 + 10A + B(where AB can be written as 10A+B)

7(2B + 3) = 3 + 10(B + 3) +B

14B + 21 = 3 + 10B + 30 + B

14B + 21 = 11B + 33

14B - 11B = 33 - 21

3B = 12

B = 4

A = B + 3

A = 4 + 3 = 7

Therefore, the two digit number is 74.