Question

the sum of the digits of a two digit number is 7 on reversing the digits the new number obtained is 9 more than original number.Find the number​

Answer 1

Step-by-step explanation:

Let the original number be

yx

; i.e., 10y+x. We know x+y=7. The number obtained by reversing the digits in

xy

, i.e., 10x+y. The second condition gives 10x+y−2=2(10y+x). Thus we have two equations:

x+y=7....(1)

8x−19y=2....(2)

Multiply the equation (1) by 19 and get

19x+19y=133.

Adding this to (2), we obtain 27x=135. This gives x=5. Hence y=7−x=7−5=2.

The required number is 25.

Answer 2

Let us represent the two (first and second digit respectively) digits that make up the number with (X) and (Y)

The two-digit number, in real sense, will be 10X + Y (Since the value of the first digit is in Tens).

Since the sum of the digits is 7, we have:

X + Y = 7 ————————————- (1)

Reversing the digits, we have: 10Y + X

Reversing the digits increases the number by 9. We have:

10Y + X = 10X + Y + 9 ———————-(2)

From equation (1), we have:

X = (7 - Y) ————————————(3)

Let us substitute (7 - Y) for X in equation (2):

10Y + 7 - Y = 10(7 - Y) + Y + 9

9Y + 7 = 70 - 10Y + Y + 9

9Y + 7 = 79 - 9Y

9Y + 9Y = 79 - 7

18Y = 72, Y = 72/18

Y = 4

Let us substitute (4) for Y in equation (3):

X = 7 - 4

X = 3.

Putting the two digits together, the two-digit number is:

34.