In a three-digit number, the digit in the unit's place is 75% of the digit in the ten's place. The digit in the ten's place is greater than the digit in the hundred's place by 1. If the sum of the digits in the ten's place and the hundred's place is 15. What is the number ?

Solution(By Examveda Team)

Let the hundred's digit = x
Then, ten's digit = (x + 1)
Unit's digit :
$$\eqalign{ & = 75\% {\text{ of }}\left( {x + 1} \right) \cr & = \frac{3}{4}\left( {x + 1} \right) \cr} $$
$$\eqalign{ & \therefore \left( {x + 1} \right) + x = 15 \cr & \Leftrightarrow 2x = 14 \cr & \Leftrightarrow x = 7 \cr} $$
So, hundred's digit = 7
Ten's digit = 8
Unit's digit :
$$\eqalign{ & = \frac{3}{4}\left( {x + 1} \right) \cr & = \frac{3}{4}\left( {7 + 1} \right) \cr & = \frac{3}{4}\left( 8 \right) \cr & = 6 \cr} $$
Hence, required number = 786