Question

A number consists of two digits whose sum is 9. If 27 is subtracted from the number, its digits are reversed. Find the number.​

Answer 1

Answer:

Let us assume, x and y are the two digits of the two-digit number

Therefore, the two-digit number = 10x + y and reversed number = 10y + x

Given:

x + y = 9 -------------1

also given:

10x + y - 27 = 10y + x

9x - 9y = 27

x - y = 3 --------------2

Adding equation 1 and equation 2

2x = 12

x = 6

Therefore, y = 9 - x = 9 - 6 = 3

The two-digit number = 10x + y = 10*6 + 3 = 63

Step-by-step explanation:

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Answer 2

Given

A number consists of two digits whose sum is 9. If 27 is subtracted from the number, its digits are reversed.

Find out

Find the number

Solution

★ Let tens digit be x and ones digit be y

• Original number = (10x + y)

According to the given condition

✞Sum of two digits number is 9

• (x + y) = 9 -----(i)

✞If 27 is subtracted from the number, its digits are reversed.

• Reversed number = (10y + x)

➟ 10x + y - 27 = 10y + x

➟ 10x - x + y - 10y = 27

➟ 9x - 9y = 27

➟ 9(x - y) = 27

➟ x - y = 3 -----(ii)

Add both the equations

➟ (x + y) + (x - y) = 9 + 3

➟ x + y + x - y = 12

➟ 2x = 12

➟ x = 12/2 = 6

Put the value of x in eqⁿ (ii)

➟ (x - y) = 3

➟ 6 - y = 3

➟ y = 6 - 3 = 3

Hence,

• Original number = 10x + y = 63
• Reversed number = 10y + x = 36

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