Question

In a two digit number, the ten’s digit is three times the unit's digit. When the number is
decreased by 54, the digits are reversed. Find the number.
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Answer 1

Answer:

The digits reversed .find the number.

Answer 2

$\huge{\underline{\boxed{\boxed{\red{\mathcal{QUESTION:}}}}}}$

In a two digit number, the ten’s digit is three times the unit's digit. When the number is  decreased by 54, the digits are reversed. Find the number.

$\huge{\underline{\boxed{\boxed{\red{\mathcal{SOLUTION:}}}}}}$

$\star{\underline{\blue{\bf{Given:}}}}$

• In a two digit number, the ten’s digit is three times the unit's digit.
• When the number is  decreased by 54, the digits are reversed.

$\star{\underline{\blue{\bf{To\;Find:}}}}$

• The Number.

Let, the unit place digit be 'x'.

And, the ten's place digit be '3x'.

⇒ Original number = 10 × (3x) + (x)

⇒ Original number = 30x + x

⇒ Original number = 31x

⇒ Reversed number = 10 × (x) + (3x)

⇒ Reversed number = 10x + 3x

⇒ Reversed number = 13x

Now, according to question. It is given that when the number is  decreased by 54, the digits are reversed.

⇒ 31 x - 54 = 13 x

⇒ 31 x - 13 x = 54

⇒ 18 x = 54

⇒ x = 54/18

⇒ x = 3

∴ Original number = 31x = 31 × 3 = 93

Hence, the number is 93.

$\star{\underline{\blue{\bf{Verification:}}}}$

Case : 1) In a two digit number, the ten’s digit is three times the unit's digit.

⇒ In number '93', unit digit = 9 and ten's digit = 3 and it is 3 times of unit digit.

Case : 2). When the number is  decreased by 54, the digits are reversed.

⇒ 93 - 54 = 39, digit are reversed.

Hence Proved!!

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