Question

The cost price of a desk and a chair is Rs. 371. If the desk costs 20% more than the chair. Find the price of each.

Answer 1

Hint: Let the price of the chair be $x$. Use the given condition to find the price of the desk. Then, the cost price of a desk and a chair is given as Rs. 371. Put the sum of cost price of desk and chair equals to Rs. 371 to find the value of $x$. Then substitute the value of $x$ in the price of desk.

Complete step-by-step answer:
Let the price of the chair be $x$, then calculate the price of the desk which is 20% more than the price of the chair.
First, we will calculate the amount more than the chair in the cost price of the desk.
20% of $x$ will be priced more than chairs.
Now, write the total cost price of the desk.
$x + 20\% \left( x \right)$
On solving the expression, we get,
$x + \dfrac{{20}}{{100}}\left( x \right) = x + \dfrac{x}{5} = \dfrac{{6x}}{5}$
Thus, the price of desk is $\dfrac{{6x}}{5}$
Given, the cost price of desk and chair was Rs. 371.
That is, $x + \dfrac{{6x}}{5} = 371$
Solve the equation by taking L.C.M and then cross- multiplying.
$
  \dfrac{{5x + 6x}}{5} = 371 \\
  \dfrac{{11x}}{5} = 371 \\
  11x = 371\left( 5 \right) \\
  x = \dfrac{{1855}}{{11}} \\
  x = 168.63 \\
$
Therefore, the price of chair is 168.83
And the price of desk can be calculated as, $\dfrac{{6\left( {168.83} \right)}}{5} = Rs.202$

Note: In this question, the price of a desk is 20% more than the price of a desk, not just 20% the price of a chair. It would be wrong to write the price of a desk as $\dfrac{x}{5}$. The price of the desk will be calculated as $x + \dfrac{x}{5} = \dfrac{{6x}}{5}$. At last, we have to substitute the value of $x$ to find the value of the desk also.