Question

A two-digit number is equal to 7 times the sum of its digits. The number formed by reversing its digits is 18 less than the original number. Find the original number.

Answer 1

Answer:

the required number is 24.

Answer 2

Let the digits be X and Y.

so,the original no. is XY=10X+Y

According to the question,

7 (X+Y)=10X+Y

7X+7Y=10X+Y

0=10X+Y-7X-7Y

0=3X-6Y..............(¡)

Now,in second statement,

XY-YX=18

It means,

10X+Y-10Y-X=18

9X-9Y=18

9(X-Y)=18

X-Y=18/9

X-Y=2

X=2+Y.............(¡¡)

Put eq.(¡¡) in eq.(¡)

3X-6Y=0

3(2+Y)-6Y=0

6+3Y-6Y=0

6-3Y=0

6=3Y

6/3=Y

Y=2

Put value of Y in eq.(¡¡)

X=2+Y

X=2+2

X=4

Hence,X=4,Y=2