Question

If the manufacturer gains 10%, the wholesale dealer 15% and the retailer 25% then find the cost of production of a table the retail price of which is Rs 1265.
(A) 600
(B) 800
(C) 700
(D) 900

Answer 1

Hint: Assume the cost of production to be some variable. Increase its value by 10%, 15% and 25% successively as per the different profits given in the question. Now compare its value with the final retail price which is also given in the question. Find the value of cost of production from this equation.

Complete step-by-step solution:
According to the question, the retail price of a table is given and the profits gained by manufacturer, wholesale dealer and retailer are also given. We have to determine the cost of production of the table.
Let the cost of production of the table is $x$ (in rupees).
On this cost of production, the manufacturer is gaining 10%. So the price will be increased by 10% here. If $C$ is denoting the price of the table then we have:
$
   \Rightarrow C = x + \dfrac{{10}}{{100}}x \\
   \Rightarrow C = x + \dfrac{x}{{10}} \\
   \Rightarrow C = \dfrac{{11}}{{10}}x
 $
Now, at this price, wholesale dealers are gaining 15%. So again the price will be increased by 15% of what it was earlier. So we have:
$
   \Rightarrow C = \dfrac{{11}}{{10}}x + \dfrac{{15}}{{100}} \times \dfrac{{11}}{{10}}x \\
   \Rightarrow C = \left( {1 + \dfrac{{15}}{{100}}} \right)\dfrac{{11}}{{10}}x \\
   \Rightarrow C = \left( {1 + \dfrac{3}{{20}}} \right)\dfrac{{11}}{{10}}x \\
   \Rightarrow C = \dfrac{{23}}{{20}} \times \dfrac{{11}}{{10}}x
 $
And finally the retailer is gaining 25% on it. So the price will again increase by 25% of what it was earlier.
$
   \Rightarrow C = \dfrac{{23}}{{20}} \times \dfrac{{11}}{{10}}x + \dfrac{{25}}{{100}} \times \dfrac{{23}}{{20}} \times \dfrac{{11}}{{10}}x \\
   \Rightarrow C = \left( {1 + \dfrac{{25}}{{100}}} \right)\dfrac{{23}}{{20}} \times \dfrac{{11}}{{10}}x \\
   \Rightarrow C = \dfrac{{125}}{{100}} \times \dfrac{{23}}{{20}} \times \dfrac{{11}}{{10}}x \\
   \Rightarrow C = \dfrac{5}{4} \times \dfrac{{23}}{{20}} \times \dfrac{{11}}{{10}}x
 $
Thus this is the final retail price in terms of initial cost of production i.e. $x$ and its value is already given in the question and it is Rs 1265. So we have:
$ \Rightarrow \dfrac{5}{4} \times \dfrac{{23}}{{20}} \times \dfrac{{11}}{{10}}x = 1265$
On solving this, we’ll get:
$
   \Rightarrow \dfrac{1}{4} \times \dfrac{{23}}{{20}} \times \dfrac{{11}}{2}x = 1265 \\
   \Rightarrow x = \dfrac{{1265 \times 4 \times 20 \times 2}}{{23 \times 11}} \\
   \Rightarrow x = 5 \times 4 \times 20 \times 2 \\
   \Rightarrow x = 800
 $

Thus the initial cost of production is Rs 800. (B) is the correct option.

Note: If a certain quantity is undergoing a successive percentage change then we can find its final value in one step only instead of solving one step for every percentage change. For example, in the above question, $x$ is undergoing a percentage increase of 10%, 15% and 25% successively. So instead of finding its final value in three different calculations, we can do it in one step as shown below:
$ \Rightarrow {\text{Final Value}} = \left( {1 + \dfrac{{10}}{{100}}} \right)\left( {1 + \dfrac{{15}}{{100}}} \right)\left( {1 + \dfrac{{25}}{{100}}} \right)x$
Here $\left( {1 + \dfrac{{10}}{{100}}} \right)$ accounts for 10% increase, $\left( {1 + \dfrac{{15}}{{100}}} \right)$ accounts for 15% increase and $\left( {1 + \dfrac{{25}}{{100}}} \right)$ accounts for 25% increase.
Thus the above problem can be solved in one step only as shown:
$ \Rightarrow \left( {1 + \dfrac{{10}}{{100}}} \right)\left( {1 + \dfrac{{15}}{{100}}} \right)\left( {1 + \dfrac{{25}}{{100}}} \right)x = 1265$