Question

On reversing the digits of a two digit number obtained is 9 less than three times the original number. If the difference of these two numbers is 45 find the original number​

Answer 1

Answer:

original number:  27

reversed number:  72

Step-by-step explanation:

Let the tens place digit = a

Let the units place digit = b

⇒ Original two-digit number = 10a + b

⇒ Reversed two-digit number = 10b + a

If the reversed two-digit number is 9 less than 3 times the original number:

⇒ 10b + a = 3(10a + b) - 9

⇒ 10b + a = 30a + 3b - 9

⇒ 7b = 29a - 9

If the different of the two numbers is 45 (and the reversed number is larger than the original number):

⇒ (10b + a) - (10a + b) = 45

⇒ 10b + a - 10a - b = 45

⇒ 9b -9a= 45

⇒ 9(b - a)= 45

⇒ b - a= 5

⇒ b = 5 + a

Substitute  b = 5 + a  into  7b = 29a - 9  and solve for a:

⇒ 7(5 + a) = 29a - 9

⇒ 35 + 7a = 29a - 9

⇒ 44 = 22a

⇒ a = 2

Finally, substitute the found value of a into  b = 5 + a  and solve for b:

⇒ b = 5 + 2 = 7

Therefore,

• original number:  27
• reversed number:  72

Answer 2

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To find :-

The original number

Given :-

The reverse of 2 digit number is 9 less than 3 times the original number

let tens digit of original number = x

ones digit = y

which means

(10y + x) + 9= 3(10x + y)

And the difference between the reverse digit and the original number is 45

(10y + x) - (10x + y) = 45

Solution :-

(10y + x) + 9 = 3(10x + y) ---------- {equation 1}

10y + x + 9 = 30x + 3y

9 = 30x - x + 3y - 10y

9 = 29x - 7y ---------- {equation 2}

(10y + x) - (10x + y) = 45 ---------- {equation 3}

10y - y - 10x + x = 45

9y - 9x = 45 (dividing whole equation by 9)

y - x = 5

y = 5 + x ---------- {equation 4}

(putting values of equation 4 in equation 2)

$9 = 29x - 7(5 + x) \\ 9 = 29x - 35 - 7x \\ 9 + 35 = 29x - 7x \\ 44 = 22x \\ \frac{44}{22} = x \\ 2 = x$

(Putting the value of x in equation 4)

y = 5 + 2 = 7

Verification :-

(Taking equation 3 and putting values of x and y)

(10y + x) - (10x + y) = 45

(10×7 + 2) - (10×2 + 7) = 45

(70 + 2) - (20 + 7) = 45

72 - 27 = 45

45 = 45

• Hence, verified.

Result :-

The original number is 27.