Question

Find the loss or gain as percent, if the c. p. Of 8 articles a, all of the same kind, is equal to s. p of 10 articles

Answer 1

AnswEr :

$\bullet\quad\textsf{CP of 8 Articles = SP of 10 Articles}\\\\ \bullet\quad\sf{CP \times 8 = SP \times 10} \\\\\bullet\quad \sf{\dfrac{CP}{SP} = \dfrac{10}{8}}\\\\\bullet\quad\sf CP = 10 \quad and \quad SP = 8$

$\rule{200}{1}$

• Loss Percentage in the Case :

$:\implies\tt Loss\% = \dfrac{Loss}{CP}\times 100\\\\\\:\implies\tt Loss\% = \dfrac{(CP-SP)}{CP} \times 100\\\\\\:\implies\tt Loss\% = \dfrac{(10 - 8)}{1\cancel0} \times 10 \cancel0\\\\\\:\implies\tt Loss\% =2\times 10 \\\\\\:\implies \pink{\boxed{\tt Loss\% =20\%}}$

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∴ Hence, Loss Percentage will be 20%.

$\rule{200}{2}$

$\boxed{\begin{minipage}{7 cm}\underline{\text{Some Important Formulae Related to it :}}\\ \\ SP=CP\times(100+\sf Profit)\%\\ \\SP=CP\times(100-Loss)\%\\ \\Profit\%=\dfrac{Profit}{CP}\times100 \\ \\Loss\%=\dfrac{Loss}{CP}\times100\end{minipage}}$

Answer 2

Question :--- Find the loss or gain as percent, if the c. p. Of 8 articles a, all of the same kind, is equal to s. p of 10 articles ...

Solution (1) :--- Lets Try it with Basic Method First .

Let CP of one article = Rs. x

Than , CP of 8 article = Rs. 8x = SP of 10 article..

Now, Cp of 10 article = Rs. 10x

Now, we know that, when CP is more than SP , we have Loss . That is given by :--

Loss = CP - SP

→ Loss = CP of 10 article - SP of 10 article

Putting value of SP of 10 article from above we get :--

→ Loss = 10x - 8x

→ Loss = Rs. 2x

So, their was a loss of Rs.2x .

Now, Profit and Loss % is always on CP .

→ Loss % = (Loss in Rs.) * 100/ (CP)

Putting values we get ,

→ Loss % = (2x) * 100 / 10x [ As Loss was on 10 articles]

→ Loss % = 20% .

Hence, in this case , we have Loss of 20% ..

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Solution (2) :--- Lets try it with Ratio Method now,. .

Given :-

→ CP of 8 article = SP of 10 article

→ 8 CP = 10 SP

→ CP / SP = 10/8

→ CP / SP = 5/4

So, CP = 5 unit , SP = 4 unit .

→ Loss = CP - SP = 5 - 4 = 1 unit

→ Loss % = Loss * 100/ CP

→ Loss % = 1 * 100 / 5 = 20% .

Hence, their will be Loss of 20% in this case.

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Solution (3) :--- Lets See Direct Formula Now ,,,

→ If CP of A article = SP of B article

and , we have , A > B ,,

Than Their will be Always Gain .

And , in This case , Gain % is Given by = [ ( A-B)*100/B ]

→ and , if we have, A < B ,,

Than, Their will be Loss Always..

And , in This case , Loss % is Given by = [ (B-A)*100/B ]

so, From Question we have,

→ A = 8

→ B = 10

Since, A < B ,

it will be Loss in This case. ( As Discuss) .

Hence, Loss % = [ (10 - 8) * 100 / 10 ]

→ Loss % = 2* 100 / 10

→ Loss % = 20% .

So, Their will be Loss of 20% ..