Question

Raju sells two apartments for equal price each. On one transaction he loses 40% and the other he gains
40%. What is his net profit or loss percentage?​

Answer 1

Answer:

Loss; 16 %

Step-by-step explanation:

Let the selling price be SP each

1st Transaction:

Selling Price: SP

Loss: 40 %

Cost Price: CP$_{1\\\\}$

So,

    $\frac{CP_{1}- SP}{CP_{1} }$ = 40%

    $\frac{CP_{1}- SP}{CP_{1} }$ = $\frac{40}{100}$

    CP$_{1}$ - SP = 0.4*CP$_{1}$

    0.6*CP$_{1}$ = SP

    CP$_{1}$ = $\frac{5SP}{3}$

   

2nd Transaction:

Selling Price: SP

Profit: 40%

Cost Price: CP$_{2\\}$

So,

    $\frac{SP - CP_{2\\}}{CP_{2\\}}$ = 40%

     $\frac{SP - CP_{2\\}}{CP_{2\\}}$ = $\frac{40}{100}$

    SP - CP$_{2}$ = 0.4*CP$_{2}$

    SP = 1.4*CP$_{2}$

    CP$_{2}$ = $\frac{5SP}{7}$

Now,

Total Selling Price = 2SP

Total Cost Price = $\frac{5SP}{3} + \frac{5SP}{7}$

                          = $\frac{35SP + 15SP}{21}$

                          = $\frac{50SP}{21}$

                          = 2.38 SP

As, Cost Price is greater than Selling Price

∴ there is a loss

Loss percentage = (Total cost price - Total selling price) / cost price * 100 %

= $\frac{ \frac{50SP}{21} - 2SP}{\frac{50SP}{21}}$ * 100 %

= $\frac{8SP}{50SP}$ * 100 %

= 16 %

This took a lot of time ^-^ Hope this helps!!