Question

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.

• A. 63
• B. 75
• C. 36
• D. 57

Answer 1

Answer: (C)

Let the ten's digit $=x$
Then unit's digit $=x+3$
$\therefore$ Original number $=10\times x+(x+3)=11x+3$

T	U
x	x+3

Number formed after reversing digits
$=10(x+3)+x$
$=10x+30+x=11x+30$

T	U
x+3	x

According to given condition
$\frac{11x+30}{11x+3}=\frac{7}{4}\Rightarrow 44x+120=77x+21$

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

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