Question

A number consists of two digits whose sum is 9. If 27 is added to the
number, the digits change their places. Find the number.
Class 10 QUESTION
MATHS​

Answer 1

Answer:

36 is the answer

Step-by-step explanation:

mark as brainliest please

Answer 2

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★ Correct Question:

• A number consists of two digits whose sum is equal to 9. If 27 is added to the original number, the digits interchange their places. Find the number

★ Required Solution:

• The number which satisfies the above mentioned statements  is 36

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★ Step by step explanation:

⋆ Given:

~ Number consists of two digits whose sum is 9 If 27 is added to the

number, the digits change their places

⋆ To Find :

~ The original number which makes the statements true$\:$

⋆ Full Solution:

• Let the unit's digit of the number be x
• Let the ten's digit of the number be y

~ According to the first condition the sum of the digits is 9

➟ㅤㅤ x + y = 9

➟ㅤㅤ y = 9 - x

~ Now as we have found the value of y in the terms of x let's find he original number

➟ㅤㅤ10( 9 - x ) + x

➟ㅤㅤ90 - 10x + x

➟ㅤㅤ90 - 9x

~ Now, if the digits interchange then,

• The tens digit will be x
• The ones digit will be 9 - x

~ So, the new number which is formed will be

➟ㅤㅤ10(x) + 9 - x

➟ㅤㅤ10x - x + 9

➟ㅤㅤ9x + 9

★ According to the question:

• Let's frame up an equation as per the 3rd statement

➞ㅤㅤ90 - 9x + 27 = 9x + 9

➞ㅤㅤ90 + 27 - 9x = 9x + 9

➞ㅤㅤ117 - 9x = 9x + 9

➞ㅤㅤ117 - 9 = 9x + 9x

➞ㅤㅤ108 = 18x

➞ㅤㅤx = 108/18

➞ㅤㅤx = 6

★ The original number:

➞ㅤㅤ90 - 9x

➞ㅤㅤ90 - 9 × 6

➞ㅤㅤ90 - 54

➞ㅤㅤ36

∴The number which makes the following true is 36

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