Question

A two-digit number is equal to 4 times the sum of its digits. If the digits of the number are reversed, the new number formed is 27 more than the original number. Find the original number.

Answer 1

Answer:

The original number is 36.

Step-by-step explanation:

Solution;

Let 10x+y be a two digit number.

By question;

10x+y=4(x+y)

or, 10x+y=4x+4y

or, 10x-4x=4y-y

or, 6x=3y

or, x=3y/6

or, x=y/2..........(i)

Similarly,

10x+y+27=10y+x

or, 10x-x=10y-y-27

or, 9x=9y-27

or, 9(y/2)=9y-27

or, 9y=2(9y-27)

or, 9y=18y-54

or, 54=18y-9y

or, 9y=54

or, y=54/9

or, y=6

Now, putting y=6 in (i)

x=y/2

=6/2

=3

Hence, the required original number is 10x+y=10x3+6=30+6=36

Answer 2

Gɪᴠᴇɴ :-

A two-digit number is equal to 4 times the sum of its digits. If the digits of the number are reversed, the new number formed is 27 more than the original number.

ᴛᴏ ғɪɴᴅ:-

• Original Number
• Reversed Number

sᴏʟᴜᴛɪᴏɴ :-

Let tens place digit be x & ones place be y

Then,

➦ Original number = (10x + y)

✞ According to 1st condition :-

➮ (10x + y) = 4(x + y)

➮ 10x + y = 4x + 4y

➮ 10x - 4x = 4y - y

➮ 6x = 3y

➮ 6x/3 = y

➮ 2x = y

➮ y = 2x. --(1)

✞ According to 2nd condition :-

➦ Reversed Number = (10y + x)

➮ (10x + y) + 27 = 10y + x

➮ 10x - x + y - 10y = -27

➮ 9x - 9y = -27

➮ 9(x - y) = -27

➮ (x - y) = -27/9

➮ (x - y) = -3. ---(2)

Put the value of (1) in (2) , we get,

➮ x - y = -3

➮ x - 2x = -3

➮ -x = -3

➮ x = 3

Put x = 3 in (1) , we get,

➮ y = 2x

➮ y = 2×3

➮ y = 6

Hence,

✞Original number(10x + y) = 10×3 + 6 = 36

✞Reversed number(10y + x) = 10×6 +3= 63