A person spends $\frac{1}{3}$ part of his income on food, $\frac{1}{4}$ part on house rent and remaining Rs. 630 on other items. the house rent is:

The correct answer is Rs.378.

Let's break down the solution step-by-step to find the house rent.

Step 1: Determine the fraction of total income spent on food and house rent.
Fraction of income spent on food = $\frac{1}{3}$
Fraction of income spent on house rent = $\frac{1}{4}$

Total fraction spent on food and house rent = $\frac{1}{3}+\frac{1}{4}$

Taking the common denominator (12):
$\frac{4+3}{12}=\frac{7}{12}$

Step 2: Calculate the remaining fraction of income.
The total income represents a whole fraction of 1 (or $\frac{12}{12}$ ).

Remaining fraction = $1-\frac{7}{12}=\frac{5}{12}$

Step 3: Find the total income.
We are given that the remaining amount spent on other items is Rs. 630.
Therefore, $\frac{5}{12}$ of the total income = Rs. 630.

Total Income = $630\×\frac{12}{5}$

Total Income = $126\×12=\text{Rs. 1512}$

Step 4: Calculate the house rent.
House rent is $\frac{1}{4}$ part of the total income.

House rent = $\frac{1}{4}\×1512=\text{Rs. 378}$

Thus, the house rent is Rs.378.