Question

the two digit number is such that the number of its digits4 . if 18 is added to the number its digits are reversed find the number

Answer 1

Hey mate!!

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Let the digit at units place be x and tens place be y.

∴ The two digit number = 10y + x.

Given, 10y + x = 4 (x + y)

=> 10y + x = 4(x + y)

=> 10y +x = 4x + 4 y

=> 10y - 4y = 4x - x

=> 6y = 3x

=> x = 2y

Also,

10y + x + 18 = 10x + y

=> 10y + x - 10x - y = -18

=> 9y - 9x = -18

=> 9(y - x) = -18

=> y - x = -2

=> y = -2 + x

=> y = -2 + 2y [x = 2y]

=> y - 2y = -2

=> -y = -2

=> y = 2

∴ x = 2y = 2 × 2 = 4

Thus, the number is 10 × 2 + 4 = 20 + 4 = 24

Thanks for the question!!

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