$A$ lends $\text{Rs. }30,000$ to $B$ at the rate of $10\%$ per annum on simple interest. After $5$ years, $B$ returned $\text{Rs. }40,000$ and a watch to settle the dues. Find the price of the watch.

Given:
Principal amount lent, $P=\text{Rs. }30,000$
Rate of simple interest, $R=10\%$ per annum
Time, $T=5\text{years}$

First, find the total simple interest ($SI$) accumulated over $5$ years:

$$SI=\frac{P\times R\times T}{100}$$

$$SI=\frac{30000\times 10\times 5}{100}=300\times 50=15,000$$

The total amount ($A$) that $B$ needs to pay after $5$ years is:

$$\text{Total Amount Due}=P+SI=30,000+15,000=45,000$$

$B$ settled the account by paying $\text{Rs. }40,000$ cash and a watch. Let the price of the watch be $W$.

$$\text{Cash Paid}+\text{Price of Watch}=\text{Total Amount Due}$$

$$40,000+W=45,000$$

$$W=45,000-40,000=5,000$$

Thus, the price of the watch is $\text{Rs. }5,000$.