Question

The ratio between a two digit number and number obtained by reversing the digits is 4:7. If the difference between the digits of the number is 3. Frame two equitation and solve them by cross method to find the two digit number.

Answer 1

Let x be the required two-digit number at ten's place.

Let y be the required two-digit number at one's place.

Therefore the decimal expansion is 10x+y.

Given that the difference between the digits of the number is 3.

x - y = 3 

y = x + 3 ------ (1)

Given that the ratio between a two-digit number and number obtained by reversing the digits is 4:7.

10x + y/10y + x = 4/7

7(10x + y) = 4(10y + x)

70x + 7y = 40y + 4x

66x = 33y

66x = 33(x+3)

66x = 99x + 99

33x = 99

x = 3.

Substitute x = 3 in (1) we get

y = x + 3

y = 6.


Therefore the required two-digit number is 36.


verification:

10x + y/10y + x = 4/7

10(3) + 6/10(6) + 3 = 4/7

30 + 6/60 + 3 = 4/7

36/63 = 4/7

4/7 = 4/7.


Hope this helps!

Answer 2

Answer:

36

Step-by-step explanation:

let x be the required number of the two digit no. at tens place

let y be the required ones place no. of the two digit no.

4:7 =4/7 is the ratio

10x+y

x-y= 3

y=x+3

10x+y/10y+x=4/7

7(10x+y)=4(10y+x)

70x+7y=40y+4x

66x=33(x+3)

66x=99x+99

33x=99

x=3

y= 3+3

=6

so the no. is 36