Question

6. Mr. Paul bought two watches for Rs. 574. He sold one watch at a profit of 25% but suffered a loss of 20% on the other. If the selling prices of both the articles are equal, find the cost price of each watch​

Answer 1

$\huge\tt{SOLUTION:}$

Given;

• Mr paul bought 2 watches for 574 rupees

• He suffered 20 % loss and 25 % gain on each watch.

• SP of both watches is same .

To find:

• CP of both watches .

Solution:

Lets assume that cost price of both watches

is x and [574-x ]

$\begin{gathered}\boxed{\sf{SP = \frac{100 \pm loss/profit}{100} \times CP}}\\\end{gathered}$

USING THE ABOVE MENTIONED FORMULA:

$\begin{gathered}\sf{\implies \frac{100+25}{100} \times [576 - x] = \frac{100-80}{100} \times [x]}\\\end{gathered}$

$\begin{gathered}\sf{\implies \frac{125}{100} \times [574-x ]= \frac{80}{100} \times [x] }\\\end{gathered}$

$\begin{gathered}\sf{\implies 80 x = 125[574 -x]}\\\end{gathered}$

$\begin{gathered}\sf{\implies 80x= 71750 - 125x }\\\end{gathered}$

$\begin{gathered}\sf{\implies 125 = 80 x = 71750}\\\end{gathered}$

$\begin{gathered}\sf{\implies 205x = 71750}\\\end{gathered}$

$\begin{gathered}\sf{\implies x = \frac{71750}{205} \implies x = 350 }\\\end{gathered}$

$574 - x = 574 - 350$

$\begin{gathered}\sf{\implies 224 }\\\end{gathered}$

So the cost price of two watches is 350 and 224 rupees