Question

A man sold two of his computers for Rs.20,000 each. On one he made a gain of 5% and on the other a loss of 10%. Find his overall gain or loss.

Answer 1

Hint: Cost price (CP) is the price at which an article is purchased.
Selling price (SP) is the price at which an article is sold.
If selling price is more than cost price, profit (gain) occurs.
If selling price is less than cost price, loss occurs.
In case of profit,
$ \Rightarrow \cos t\;price = \;\dfrac{{100\;{\rm X}\;selling\;price}}{{100 + profit\,percentage}}...........(1)$
In case of loss,
$ \Rightarrow \cos t\;price = \;\dfrac{{100\;{\rm X}\;selling\;price}}{{100 - loss\,percentage}}$

Complete step-by-step answer:
Given, the selling price of first computer are = Rs 20,000
Given, the gain on the first computer =5%
So, Cost price of first computer by using formula (1) provided in hint
$
   \Rightarrow \cos t\;price = \;\dfrac{{100\;{\rm X}\;20000}}{{100 + 5}} \\
   \Rightarrow \cos t\;price = \;\dfrac{{\;2000000}}{{105}} \\
   \Rightarrow \cos t\;price = \;19047.62................(2) \\
 $
So, the cost price of first computer is Rs. 19,047.62
Given, the selling price of second computers are = Rs 20,000
Given, the loss on the Second computer = 10 %
So, Cost price of second computer by using formula (1) provided in hint
$
   \Rightarrow \cos t\;price = \;\dfrac{{100\;{\rm X}\;20000}}{{100 - 10}} \\
   \Rightarrow \cos t\;price = \;\dfrac{{\;2000000}}{{90}} \\
   \Rightarrow \cos t\;price = \;22222.22...................(2) \\
 $
So, the cost price of second computer is Rs. 22,222.22

Now using the values of cost price of two computers from equation (2) and (3)
Total Cost price of two computers =$19047.62 + 22222.22 = 41269.84$
Total Cost price of two computers = Rs. 41,269.84
Total Selling price of two computers =$20000 + 20000 = 40000$
Total selling price of two computers = Rs 40,000
Loss = Cost price – Selling price= $41269.84 - 40000 = 1269.84$
Total Loss on selling the two computers = Rs 1269.84

Note: One can generate a profit only if $Selling Price> Cost Price$
One generates a loss when $Selling Price < Cost Price$.