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Integers

In a two digi...

Question

In a two digit no of a units place is less than digit of ten's place by 4 . If number is divided by sum of the digit the quotient is 7 , then find the number

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Solution

Let the number be $a \times 10 + b = 10 a + b$
From the given conditions
$a - b = 4$
$\frac{10 a + b}{a + b} = 7 ⟹ 3 a = 6 b ⟹ a = 2 b$
$⟹ b = 4, a = 8$
The number is $84$

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