Question

a number consists of two digits , the sum of whose digits is 9 if 4 times the original number is equal to 7 times the number obtained by reversing the digits,find the original number​

Answer 1

Step-by-step explanation:

Let, the ten's digit place be 'x' and unit digit's be 'y'

The number=10x+y

ATQ,

x+y=9------(i)

Now,

4(10x+y)=7(10y+x)

40x+4y=70y+7x

40x-7x=70y-4y

33x=66y

33x-66y=0

11(3x-6y)=0

3x-6y=0-----(ii)

Multiplying (i) with 6 we get,

6x+6y=54----(iii)

Adding (i) and (iii) we get,

3x-6y=0

6x+6y=54

________

9x=54

x=6

Substituting x=6 in equation (i) we get

x+y=9

6+y=9

y=3

Therefore, the original number=10x+y

(10×6)+3

63 (Ans)

Answer 2

Answer:

Let 'x' be the digit in the tens' place and 'y' be the digit in the unit's place...

According to the given question....

x+y=9.... (1)

The 2-digit number can be expressed as ,

10(x) +1(y)

Hence the 2-digit number is 10x+y, It is given in the question that 4 times the original number is 7 times the number formed by reversing the digits.

Hence when the digits are reversed 'y' will occupy the tens' place a 'x' will occupy the unit's place. Hence the number formed by reversing the digits would be,

10(y)+1(x)

Hence the reversed number is 10y+x

Therefore the equation is,

4(10x+y) =7(10y+x)

40x+4y=70y+7x

40x-7x+4y-70y=0

33x-66y=0

33(x-2y) =0

x-2y=0/33

x-2y=0.... (2)

Subtracting equation (2) from (1), we get,

3y=9

y=3

Substituting "y=3" in any of the equations,we get,

x=6

Hence the required number is 63.