In a two digit number unit's digit is 3 more than ten's digit. The number formed by interchanging the digits and the original number are in the ratio 7:4. Find the number.

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Solution

The correct option is C 36
Let the ten's digit $= x$
Then unit's digit $= x + 3$
$∴$ Original number $= 10 \times x + (x + 3) = 11 x + 3$
T U
x x+3
Number formed after reversing digits
$= 10 (x + 3) + x$
$= 10 x + 30 + x = 11 x + 30$
T U
x+3 x
According to given condition
$\frac{11 x + 30}{11 x + 3} = \frac{7}{4} \Rightarrow 44 x + 120 = 77 x + 21$

$\Rightarrow 77 x - 44 x = 120 - 21 \Rightarrow 33 x = 33 \Rightarrow x = 3$

The number $= 11 \times 3 + x = 33 + 3 = 36$

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