Find the total price of all three items

Given the average price of 3 furniture items is $\text{Rs } 16875$. Using the total sum formula $\text{Total} = \text{Average} \times n$:

$\text{Total Price} = 16875 \times 3 = 50625$

Represent prices using the given ratio

The ratio of their prices is given as $3: 5: 7$. Let the prices of the items be $3x$, $5x$, and $7x$. The sum of these prices equals the total price calculated:

$3x + 5x + 7x = 50625$

Solve for the value of 1 ratio part ($x$)

Combine the ratio terms and divide the total price by the sum of ratio parts ($15$):

$15x = 50625 \implies x = \frac{50625}{15} = 3375$

Calculate the price of the cheapest item

The cheapest item corresponds to the smallest ratio part, which is $3x$. Substitute $x = 3375$:

$\text{Price of cheapest item} = 3 \times 3375 = 10125$