Question

The ratio of tens digit to units digit of a two digit number is 2:3.If 27 is added to the number, the digits interchange their places.Find the number.

Answer 1

EXPLANATION.

• GIVEN

ratio of tens digit to unit digit of the two digit

number = 2:3

if 27 is added to the number the digit interchange their place.

Find the number,

according to the question,

Let the unit place = x

Let tens place = y

original number = 10x + y

reversing number = 10y + x

ratio of tens digit to unit digit of the two digit

number = 2:3

$\bold{\frac{2}{3} = \frac{x}{y} }$

2y = 3x

3x - 2y = 0 ......(1)

if 27 is added to the number the digit

interchange their place.

10x + y + 27 = 10y + x

9x - 9y = -27

x - y = -3 ......(2)

From equation (1) and (2) we get,

multiply equation (1) by 1

multiply equation (2) by 2

we get,

3x - 2y = 0

2x - 2y = -6

we get,

x = 6

put the value of x = 6 in equation (1)

we get,

3(6) - 2y = 0

18 - 2y = 0

y = 9

The number are = 10x + y

10(6) + 9 = 69

The number is = 69

Answer 2

Given ,

• The ratio of tens digit to units digit of a two digit number is 2 : 3

• If 27 is added to the number , the digits interchange their places

Let ,

The unit's digit be " x "

The ten's digit be " y "

Then , Original number = " 10x + y "

According to the question ,

x/y = 2/3

3x = 2y

3x - 2y = 0 --- (i)

And

10x + y + 27 = 10y + x

9x - 9y = -27

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

Multiply eq (ii) by 3 , we get

3x - 3y = -9 --- (iii)

Subtract eq (i) from eq (iii) , we get

3x - 3y - (3x - 2y) = -9 - 0

-3y + 2y = -9

-y = -9

y = 9

Put the value of y = 9 in eq (i) , we get

3x - 2(9) = 0

3x - 18 = 0

3x = 18

x = 18/3

x = 6

$\therefore \underline{ \sf{The \: original \: number \: is \: 69}}$