MathematicsThe sum of the digits of a two-digit number is 5. The digit obtained by increasing the digit in tens’ place by unity is one-eighth of the number. Find the number.

The sum of the digits of a two-digit number is $5$ . The digit obtained by increasing the digit in tens' place by unity is one-eighth of the number. Find the number.

A
Less than $30$
B
Lies between $30$ and $40$
C
More than $37$
D
Lies between $40$ and $50$

Solution:

Given, the sum of the digits of a two-digit number is

5

.
The digit obtained by increasing the digit in tens' place by unity is one-eighth of the number.
Let the digit at tens’ place be

x

.
Let the digit at units place be

y

x + y = 5

Also,

x + 1 = \frac{1}{8} (10 x + y)

⇒

8 x + 8 = 10 x + y

⇒

2 x + y = 8

.........(2)
Subtract (1) from (2),

2 x - x + y - y = 8

⇒

x = 3

Putting the value of

x

in (2) we get,
⇒

y = 2

Therefore, the number is

32

.
Hence, the correct option is 2.

The sum of the digits of a two-digit number is $5$ . The digit obtained by increasing the digit in tens' place by unity is one-eighth of the number. Find the number.

Solution:

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