Question

32 times of a two digit number is 23 times the number obtained by reversing its digits. The sum of its digit is 15. Find the number.

Answer 1

Answer:

69

Step-by-step explanation:

Let the number be 10x + y and the reversed number be 10y + x

x + y = 15 I.e. x = 15 - y

32(10x + y) = 23(10y + x)

320x + 32y = 230y + 23x

Substituting 15 - y as x,

320(15-y) + 32y = 230(15-y) + 23x

4800 - 320y + 32y = 230y + 345 - 23y

4800 - 345 -320y + 32y = 230y - 23y

4455 - 288y = 207y

4455 = 207y + 288y

4455 = 495y

I.e. y = 4455/495 = 9

x = 15 - y = 15 - 9 = 6

I.e. required number = 10x + y = 10×6 + 9

= 60 + 9 = 69