Question

Sum of two digit number is 24 times the sum of the reciprocal of the digit, if sum of the reciprocal of the digit is 5/12 find digit

Answer 1

Let the digits be x and y.

Then, x + y = 24 (1/x + 1/y)

Also, it is given that 1/x + 1/y = 5/12

Therefore, x + y = 24 * 5/12 = 2 * 5 = 10

From the equation 1/x + 1/y = 5/12, we get

(y + x)/xy = 5/12

x + y = 5 / 12 xy

But, x + y = 10

Thus, 10 = 5 / 12 xy

or xy = 24.

This gives, x = 24 / y.

Substituting the value of x in x+y = 10, we get

24/y + y = 10 or

y^2-10y+24 = 0

or y^2-6y-4y+24 = 0

y(y-6)-4(y-6) = 0

or (y-4)(y-6) = 0

This gives, y -6 = 0 or y-4 = 0

Therefore, y = 6 or y = 4.

If y = 6, then x = 4 and if y = 4, then x = 6.

Therefore, the numbers can be 46 or 64.