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Word Problem 11 (Gain or loss percentage)

Problem 11: The cost price of 21 articles is equal to selling price of 16 articles. Find the gain or loss percentage,

a. 33.13% gain            b. 33-1/4 % loss                      c. 25% gain                           d. 25% loss

(Actuarial analysis)

Solution:

Let cost price of each one article is ‘y’ Rs.

then;

Cost Of 21 Articles= 21y

Since cost price of 21 articles is given equal to selling price of 16 article, so

Selling Price Of 16 Articles= 21y

\Rightarrow Selling Price of One Article = \frac{21y}{16}

Here we can see that for one article the sale price 21y/16 is greater that its cost price ‘y’. So obviously a profit will be earned !

Now we know that profit is calculated by subtracting sale price from cost price;

i-e Profit = Sale Price- Cost Price

So, for one article the profit will be calculated by subtracting its sale price from its cost price;

\Rightarrow Profit = \frac{21y}{16}-y

\Rightarrow = \frac{5y}{16}

So, Profit for one article is 5y/16 Rs

Now we calculate the %age which this profit amount makes !

We know;

 Profit%age= \frac{Profit}{Cost}\times 100

\Rightarrow Profit%age= \frac{\frac{5y}{16}}{y}\times 100

\Rightarrow Profit%age= \frac{5y}{16y}\times 100

\Rightarrow Profit%age= \frac{500}{16}

\Rightarrow Profit%age= 33\frac{1}{4}%

So the profit %age is 33-1/4 %

 

 

 

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