Question

A number of two digits whose sum is 9 lf the digits are reversed the new number is 3/8 of the first number find the number

Answer 1

Answer:

72

Step-by-step explanation:

If you add the digits, it will be 9. Reverse 72, it will be 27. 27 is 3/8 of 72

Answer 2

✬ Original Number = 72 ✬

Step-by-step explanation:

Given:

• A number contains two digits.
• Sum of digits of number is 9.
• If the digits are reversed the new number is 3/8 times the original.

To Find:

• What is the number ?

Solution: Let the ones digit be y and tens digits be x. Therefore, number will be 10x + y.

➟ ( Ones + tens ) digit = 9

➟ y + x = 9

➟ x = (9 – y)................i

Now , after reversing the digits of number then reversed number formed is

• Reversed number = 10y + y

A/q

• Reversed number is 3/8 times the original number.

$\implies{\rm }$ 3/8(10x + y) = (10y + x)

$\implies{\rm }$ 30x + 3y = 8(10y + x)

$\implies{\rm }$ 30x + 3y = 80y + 8x

$\implies{\rm }$ 30x – 8x = 80y – 3y

$\implies{\rm }$ 22x = 77y

$\implies{\rm }$ 22x – 77y = 0

$\implies{\rm }$ 11(2x – 7y) = 0

$\implies{\rm }$ 2x – 7y = 0........ii

Now put the value of x in equation (ii).

➮ 2 × (9 – y) – 7y = 0

➮ 18 – 2y – 7y = 0

➮ 18 – 9y = 0

➮ 18/9 = y

➮ 2 = y

Now, put the value of y in equation (i)

➮ x = 9 – 2

➮ x = 7

• Original number is 10(7) + 2 = 72

Hence the number is 72.