Question

2. The ratio of tens digit to the ones digit of a two-digit number is 3:4. If 18
is added to the number, the digits interchange their places, find the number​

Answer 1

$\underline{\underline{\huge{\gray{\tt{\textbf Answer :-}}}}}$

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$\sf\large\bold{\orange{\underline{\blue{ Given :-}}}}$

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• The ratio of tens digit to the ones digit of a two-digit number is 3:4

• If 18 is added to the number, the digits interchange their places

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$\sf\large\bold{\orange{\underline{\blue{ To \: Find :-}}}}$

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• The number

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$\sf\large\bold{\orange{\underline{\blue{ Solution :-}}}}$

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Given that , The ratio of tens digit to the ones digit of a two-digit number is 3:4

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• Let the ten's digit be '3a'

• Let the one's digit be '4a'

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$\underline{ \underline{\bold{\texttt{Original number :}}}}$

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➠ 10(3a) + 4a ⚊⚊⚊⚊ ⓵

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$\underline{ \underline{\bold{\texttt{Reversed number :}}}}$

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➠ 10(4a) + 3a

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Also given that , If 18 is added to the number, the digits interchange their places

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So,

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: ➜ 10(3a) + 4a + 18 = 10(4a) + 3a

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: ➜ 30a + 4a + 18 = 40a + 3a

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: ➜ 34a + 18 = 43a

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: ➜ 43a - 34a = 18

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: ➜ 9a = 18

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: ➜ $\sf a = \dfrac { 18 } { 9 }$

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: ➜ a = 2 ⚊⚊⚊⚊ ⓶

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⟮ Putting a = 2 from ⓶ to ⓵ ⟯

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: ➜ 10(3a) + 4a

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: ➜ 10[3(2)] + 4[2]

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: ➜ 10(6) + 8

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: ➜ 60 + 8

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: : ➨ 68

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• Hence the number is 68