Question

The ratio of a two digit number to the number obtained by reversing it's digits is 4:7 . The sum of digits is 9 ,find the number.

Answer 1

Answer:

the number for the given problem is 36

Answer 2

Answer:-

The number is 36.

Given:

• The ratio of a two digit number to the number obtained by reversing it's digit is 4:7.

• The sum of the digits is 9.

To find:

The number.

Solution:

Let ten's place of a two digit number be x and it's unit's place be y.

$\sf{\therefore}$ Original number =10x+y

$\sf{\therefore}$ Number formed by reversing

the digit =10y+x

According to the first condition.

$\sf{\frac{10x+y}{10y+x}=\frac{4}{7}}$

$\sf{\therefore}$ 7(10x+y)=4(10y+x)

$\sf{\therefore}$ 70x+7y=40y+4x

$\sf{\therefore}$ 70x-4x+7y-40y=0

$\sf{\therefore}$ 64x-33y=0...(1)

According to the second condition

x+y=9...(2)

Multiply equation (2) by 33

33x+33y=297...(3)

Add equations (1) and (3)

64x-33y=0

+

33x+33y=297

___________

99x=297

$\sf{\therefore{x=\frac{297}{99}}}$

$\sf{\therefore}$ x=3

Substitute x=3 in equation (2)

3+y=9

$\sf{\therefore}$ y=9-3

$\sf{\therefore}$ y=6

$\sf{\therefore}$ Number=10(3)+6=36

The number is 36.