Question

the number has two digits . the digit at tens place ,is four times the digit at unit place if 54 subtracted from the number , the digit are reversed .find the number.​

Answer 1

Answer:

let the no. is 10y+x.

then, y = 4(x)

y= 4x~ (i)

then, 10y+x-54= 10x+y

10y+x-10x-y =54

9y-9x= 54

9 (y-x)=54

(y-x)=54÷9

(y-x)=6~(ii)

then, from (i)-

4x-x=6

3x=6

x=6÷3

x=2.

now, this value put in(i)-

y= 4 (2)

y= 8.

then, the no. is- 10 (8)+(2)

=80+2

=82.

Answer 2

Let the digit at Tens place be x

The digit at unit place be y

The Number is 10x + y

ACCORDING TO THE QUESTION :-

x = 3y ... eq. 01

• According to the second condition :

10x + y - 54 = 10y + x

=> 9x - 9y = 54

=> 9(x - y) = 9 × 6

=> x - y = 6 ... eq.02

• Now we can solve the Equation 01 and 02 by substitution Method :-

x - y = 6

=> 3y - y = 6 [ from eq.01 , x = 3y ]

=> 2y = 6

=> y = 3

• Now we can substitute the value of y in eq. 01 to get value of x

x = 3y

=> x = 3 × 3

=> x = 9

Hence the number is

Hence the number is 10x + y = 90 + 3 = 93