Question

the ratio of tens digit tp the unit digit of two digit number is 2:3.if 27is added to the number the digits interchange their places , find the number

Answer 1

$let \: them \: be \: 2x \: and \: 3x \\ when \: we \: write \: it \: like \: a \: \\ number \: we \: write \\ 2x \times 10 + 3x = 20x + 3x = 23x \\ given \\ 23x + 27 = 32x \\ 27 = 32x - 23x \\ 27 = 9x \\ x = \frac{27}{9} \\ x = 3 \\ 2x = 3 \times 2 = 6 \\ 3x = 3 \times 3 = 9 \\ so \: the \: number \: is \: 69 \\ if \: we \: add \: 27to \: 69 \: we \: get \: 96 \: \\ so \: 69 \: is \: correct \: answer$
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