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​
step by step solve
please ​

Answer 1

Answer:

Step 1 :Let the unit’s digit be x

Step 2 :Then, ten’s digit = (9 – x)

∴ Number = 10 × (9 – x) + x

⇒ 90 – 10x + x = (90 – 9x)

Step 3 :Adding 27 to the number 90 – 9x, we get 117 – 9x

Step 4 :Number with digits interchanged is 10x + (9 – x) = 9x + 9

Step 5 :117 – 9x = 9x + 9

Step 6 :Therefore unit’s digit = 6 and ten’s digit = 3

Step 7 :Hence the number = 36.

Answer 2

Step 1 :Let the unit’s digit be x

Step 2 :Then, ten’s digit = (9 – x)

∴ Number = 10 × (9 – x) + x

⇒ 90 – 10x + x = (90 – 9x)

Step 3 :Adding 27 to the number 90 – 9x, we get 117 – 9x

Step 4 :Number with digits interchanged is 10x + (9 – x) = 9x + 9

Step 5 :117 – 9x = 9x + 9

Step 6 :Therefore unit’s digit = 6 and ten’s digit = 3

Step 7 :Hence the number = 36.

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