Question

A number of two digits exceeds four times the sum of its digits by 6 and it is increased by 9 on reversing the digits .find the number

Answer 1

Answer:

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Step-by-step explanation:

Let t = tens digit

u = unit digit

10t+u = the number

10u+t = the reversed number

The number of two digit exceeds 4 times the sum of the digits by 3

10t+u = 4(t+u)+3

If 36 is added to the number the digits are reversed

10u+t = 10t+u+36

9u = 9t+36

u = t+4

Substitute u with t+4

10t+t+4 = 4(t+t+4)+3

11t+4 = 4(2t+4)+3

11t+4 = 8t+19

3t = 15

t = 5

u = 9

∴The number is 59.

∴Check

59+36 = 95

95 = 95

59 = 4(9+5)+3

59 = 4(14)+3

59 = 56+3

59 = 59