Question

5. The ratio between two digit number and sum of the digits is 6: 1. If the digit at the tens place is greater than the digit at unit place by 1 then find number. ​

Answer 1

Answer:-

Let the digit at ten's place be x and digit at ones place be y.

So, the number will be 10x + y.

Given:-

Ratio of two digit number and the sum of its digits = 6 : 1

i.e.,

(10x + y) : (x + y) = 6 : 1 -- equation (1)

Also given,

Digit at tens place is greater than units digit by 1.

⟹ x = y + 1 -- equation (2).

Substitute x = y + 1 in equation (1)

⟹ [ 10(y + 1) + y ] : (y + 1 + y) = 6 : 1

⟹ (10y + 10 + y) : (2y + 1) = 6 : 1

⟹ (11y + 10) / (2y + 1) = 6/1

On cross multiplication we get,

⟹ 11y + 10 = 6(2y + 1)

⟹ 11y + 10 = 12y + 6

⟹ 10 - 6 = 12y - 11y

⟹ y = 4

Now, Substitute y = 4 in equation (2)

⟹ x = y + 1

⟹ x = 4 + 1

⟹ x = 5

∴ Required number = 10x + y = 10(5) + 4 = 50 + 4 = 54.

Answer 2

Given :

• The ratio between two digit number and sum of the digits is 6: 1.
• The digit at the tens place is greater than the digit at unit place by 1

To find :

• The required number

Assume that :

Let the two digits number is

• = 10x+y

Here,

According to the 1st condition given in question,

• The ratio between two digit number and sum of the digits of the number is 6: 1.

$\sf \implies{10x + y:( x + y ): 6: 1}$

According to the 2nd condition given in question,

• If the digit at the tens place is greater than the digit at unit place by 1 that is

Digits at 10's place = Digits at unit place +1

Then,

$\sf \implies{x = y + 1}$

Or

$\sf \implies{x - 1= y}$

Solution :

$\sf \implies{ \frac{10x+y}{x + y} = \frac{6}{1} }$

$\sf \implies{ \frac{10x+x - 1}{x + x - 1} = \frac{6}{1} }$

$\sf \implies{ \frac{11x - 1}{2x - 1} = \frac{6}{1} }$

$\implies\sf{11x - 1 = 6(2x - 1)}$

$\implies\sf{11x - 1 = 12x - 6}$

$\implies\sf{ - 1 + 6 = 12x - 11x}$

$\bf \large\boxed{5 = x}$

Now,

• Here we get the value of x now place this value of x = 5 in 10x+y

$\sf \implies{10x + y}$

$\sf \implies{10 \times (5) +(x - 1)}$

$\sf \implies{50 +(5- 1)}$

$\sf \implies{50+4}$

$\bf \implies \large\boxed{54 }$

Therefore,

• The required number is 54