Question

when 75% o f two digit number is added to it the digits of the number are reversed.find the ratio of unit digit to the ten's digit in the original number

Answer 1

Let the number be 10x+y

Then, according to the question

(10x+y)+75% of (10x+y) = 10y+x

10x+y+3/4(10x+y) = 10y+x

9x+30x/4+3y/4 = 9y

(36x+30x+3y)/4 = 9y

66x+3y = 36y

66x = 33y

x/y = 1/2

Answer 2

Answer:

2:1

Step-by-step explanation:

Let x be the digit on the tens place and y be the digit on the unit place of the number,

Thus, the original number = 10 x + y,

After reversing the digit, the new number = 10 y + x,

According to the question,

Original number + 75 % of original number = New number

⇒ ( 10x + y ) + 75 % of (10x + y) = 10y + x

⇒ 10x + y + 0.75(10x+y) = 10y + x

⇒ 10x + y + 7.5x + 0.75y = 10y + x

⇒ 16.5x = 8.25y

$\implies \frac{y}{x}=\frac{16.5}{8.25}=\frac{2}{1}$

Thus, the ratio of unit digit to the ten's digit in the original number is 2 : 1.