Question

The ratio between a two-digit number and the sum of the digits of that number is 14 : 5. if the digit in the unit’s place is 6 more than the digit in the ten’s place. what is the sum of the digits of that number?

Answer 1

Answer:

Let xy denote the two digit number so that x is in ten place and y is in unit place. Therefore,

The number is 10x + y and the sum of the digits is x + y

To find the number xy? By hypothesis,

(10 x + y)/(x + y) = 14/5

Cross-multiplying,

50 x + 5y = 14 x + 14 y

Transpose 4x to LHS and y to LHS and get

36 x = 9 y

Dividing through by 9,

4x = y…………………………..…………….(1)

It is given in the question that digit in unit place is 6 more than the digit in tens place. This gives us the second equation

y = x + 6…………………………………..…(2)

Substituting for y = x+ 6 from (2) into (1),

4x = x+6

Transposing x to left,

x = 2

Putting x= 2 in (2),

y = 4x

y= 8

Using the above values of x and y,

The number is 28 (Proved)

Verification:

Sum of the digits in the number = 2+8 = 10

The number represented by xy = 10x2 + 8 =28

Sum of ratio of the number to sum of digits in number 36 = 28/10 = 14/5

So all the conditions given in the question are satisfied.

Step-by-step explanation: