Question

A number consists of two digits whose sum is 9.If 29 is subtracted from the number its digits are reserved Find the number

Answer 1

Correct 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.

Required number:

• 10x + y

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★ Sum of the digits is 29.

→ x + y = 9⠀⠀.... [1]

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After Interchanging it's digit place

• 10y + x

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★ If 29 is subtracted from the number its digits are reserved.

→ 10x + y - 27 = 10y + x

→ 10x - x + y - 10y = 27

→ 9x - 9y = 27

→ x - y = 3⠀⠀.... [2]

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From [1] and [2]

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⠀⠀⠀⠀⠀⠀x + y = 9

⠀⠀⠀⠀⠀⠀x - y = 3

⠀⠀⠀⠀⠀- ⠀ +⠀⠀-

⠀⠀⠀⠀⠀━━━━━━━━━━

⠀⠀⠀⠀⠀⠀⠀⠀⠀2y = 6

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀y = 3

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Substituting the value of y in [1]

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→ x + 3 = 9

→ x = 9 - 3

→ x = 6

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We have the value of x and y.

So, the required number will be

• 10(6) + 3 = 60 + 3 = 63

⠀

Hence,

• The required number is 63.

Answer 2

Question:-

1. A number consists of two digits whose sum is 9. If 29 is subtracted from the number its digits are reserved. Find the number.

To find,

• The number which is reserved

Solution:-

Let the unit digit of number = x

   Then the tens digit of number = y - n

So the number is         10(9 - n) + n

                                   = 90 - 9n

According to the question,

           After reserving the digit the number will be = 10x (9-n)

                                                                                   = 9n + 9

        90 - 9x = 9x + 9 + 27

        18x = 90 - 9 - 27

        18x = 54

        $\rm x= \dfrac{54}{18}=3$

Unit digit = 3

Tens digit = 9 - 3 = 6

The number is = 10 x 6 + 3 = 63

Required answer:-

• 63 is the required number