Question

A two digit number is 4 times the sum of the digits. If we interchange the digits, the number obtained is 9 less than 4 times the original number. Frame the 2 simultaneous equations for the given 2 conditions

Answer 1

Answer:

The two-digit number consists of ten’s place and units place. Let us suppose, x is ten’s place digit and y is the unit place digit

The two-digit number consists of ten’s place and units place. Let us suppose, x is ten’s place digit and y is the unit place digitSo, the 2-digit number is 10*x + y

Step-by-step explanation:

Given,

The number is four times the sum of its digits => 10*x + y = 4(x+y)

if interchanged, the number is 9 less then 4 times the original number

interchanged number = y*10 +x

original number = x*10 + y

=> y*10 + x = 4(x*10+y) - 9

So, we got the equations

10x + y = 4x + 4y —————————-(1)

10y + x = 40x + 4y - 9 ————————(2)

=>

(10–4)x = (4–1)y => 6x = 3y => 2x = y —————(3)

(40–1)x = (10–4)y +9 => 39x -6y = 9 —————-(4)

substitute eq3 in eq4

39(x) - 6(2x) = 9

(39–12)x = 9

27x = 9

x = 9/27 = 1/3

y = 2(x) = 2(1/3) =2/3

so the value of x and y is 1/3 and 2/3 respectively

and

The 2-digit number is 10*x + y = (10*1/3) + 2/3 = 12/3 = 4.

Answer 2

Step-by-step explanation:

From first condition

10y +X =4(y+x)

10 y +x =4y +4x

x-4x +10y-4y=0

-3x+6y=0

-3x =-6y

x=2y

From second condition

10x + y = 2 (10y +x) -9

10x +y = 20 y +2x-9

10x-2x+y -20y= -9

8x -19y =-9

x=2y

substituting x=2y equation (1)

16 y -19y = -9

-3= -9

y=3

original two digit number

=10y + x = 10× 3 +6

=36

-dik24