A dealer sold a camera for Rs. 1080 gaining $\dfrac{1}{8}$ of its cost price. Find:
i).the cost price of the camera
ii).the gain percent earned by the dealer

Answer Verified Verified
Hint: Using the selling price given in the question we find the relation between in cost price and selling price. Then we compute gain and gain percent.

Complete step-by-step answer:
(i) Let the cost price of the camera be x.
   Given Data: Selling Price = 1080
    Profit = $\dfrac{1}{8}$ of cost price
               = $\dfrac{{\text{x}}}{8}$
Profit implies, Selling Price = Cost Price + Profit
⟹1080 = x + $\dfrac{{\text{x}}}{8}$
⟹1080 = $\dfrac{{{\text{8x + x}}}}{8}$
⟹1080 = $\dfrac{{{\text{9x}}}}{8}$
⟹120 = $\dfrac{{\text{x}}}{8}$
⟹960 = x
Cost price of the camera x = Rs. 960

(ii) Gain = $\dfrac{{\text{x}}}{8}$ = $\dfrac{{960}}{8}$
⟹Gain = Rs. 120

Gain percent (gain %) = ($\dfrac{{{\text{gain}}}}{{{\text{cost price}}}}$) × 100
                             = ($\dfrac{{120}}{{960}}$) *100
                             = 100/8
Gain % = 12.5 %

Note – In order to solve this type of question, the crucial step is to find the relation between selling price and cost price.
If Profit: Selling price = Cost Price + Profit
If Loss: Selling Price = Cost Price – Loss
Profit or loss will always be a fraction or percentage of cost price.
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