Question

12. The sum of the digits of a two digit number is 7.
If the digits are reversed, the number is reduced
by 27. Find the number
​

Answer 1

Answer:

52 and 25

Step-by-step explanation:

Follow the image to get a clear idea

Answer 2

✯ The number = 52 ✯

Step-by-step explanation:

Given:

• The sum of the digits of two digit number is 7.
• If the digits are reversed, the number is reduced by 27.

To find:

• The number.

Solution:

Let the unit's digit of the number be x and the ten's digit of the number be y.

Then,

• The number = 10y+x

✯ ${\underline{\sf{According\:to\:the\:1st\: condition:-}}}$

• The sum of the digits of two digit number is 7.

$\implies\sf{x+y=7}$

$\implies\sf{x=7-y.............eq(1)}$

✯ ${\underline{\sf{According\:to\:the\:2nd\: condition:-}}}$

• If the digits are reversed, the number is reduced by 27.

$\implies\sf{10x+y=10y+x-27}$

$\implies\sf{10x-x+y-10y=-27}$

$\implies\sf{9x-9y=-27}$

$\implies\sf{9(x-y)=-27}$

$\implies\sf{x-y=-3}$

• [ Put x = 7-y from eq (1) ]

$\implies\sf{7-y-y=-3}$

$\implies\sf{-2y=-10}$

$\implies\sf{y=5}$

Now put y = 5 in eq(1).

x = 7-5

→ x = 2

Therefore,

The number = 10×5 + 2 = 52

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