Question

cycle.
7.
The cost price of 25 decoration pieces is same as the selling price of 35 decoration piece.Find
the gain or loss per cent.​

Answer 1

Clarification:

Here, we are provided that cost price of 25 decoration pieces is same as the selling price of 35 decoration piece. So, we aren't given the exact price. At first we'll find the LCM of decoratio tion prices and will take it as cost price of 25 decoration and selling price of 35 decoration piece.

Then, we'll find cost price of 1 decoration piece and selling price of 1 decoration piece. If CP will be more, then there is loss & if SP will be more ,then there'll be profit.

After that, if we get loss/profit then we'll find the loss% or gain % by the formula in order to get the answer.

Given:

• CP of 25 decoration pieces = SP of 35 decoration pieces.

To calculate:

• Gain % or loss %

Calculation:

$\sf { LCM \: of \: 25 \: \& \: 35 = 175}$

Let,

• CP of 25 articles be Rs 175.

→ CP of 25 articles = Rs 175

→ CP of 1 article = $\sf {Rs \: \dfrac{175}{25}}$

→ CP of 1 article = Rs 7

Also, let,

• SP of 35 articles be Rs 175.

→ SP of 35 articles = Rs 175

→ SP of 1 article = $\sf {Rs \: \dfrac{175}{35}}$

→ SP of 1 article = Rs 5

Clearly,

• Cost price > Selling price

So, here is loss.

→ Loss = CP - SP

→ Loss = Rs ( 7 - 5 )

→ Loss = Rs 2

Hence,he/she got the loss of Rs 2.

Now, Calculating gain % :

As we know that,

$\star \: \: {\underline {\boxed {\large {\sf \pink { Loss \: \% = \Bigg ( \dfrac{Loss}{CP} \times 100 \Bigg ) \% } }}}} \\ \\ \\ \sf{\longrightarrow \: Loss \: \% = \Bigg ( \dfrac{2}{7} \times 100 \Bigg ) \%} \\ \\ \\ \sf{\longrightarrow \: Loss \: \% = \Bigg ( \dfrac{200}{7} \Bigg ) \%} \\ \\ \\ \longrightarrow \underline{\boxed{\sf{Loss \: \% = 28.57 \: \%}}} \: \red{\bigstar}$

Hence, loss % is 28.57 %.

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$\small\boxed{ \begin{array}{cc}\large\sf\dag \: {\underline{More \: Formulae}} \\ \\ \bigstar \: \sf{Gain = S.P – C.P} \\ \\ \bigstar \:\sf{Loss = C.P – S.P} \\ \\ \bigstar \: \sf{Gain \: \% = \Bigg( \dfrac{Gain}{C.P} \times 100 \Bigg)\%} \\ \\ \bigstar \: \sf{loss \: \% = \Bigg( \dfrac{loss}{C.P} \times 100 \Bigg)\%} \\ \\ \bigstar \: \sf{S.P = \dfrac{100+Gain\%}{100} \times C.P} \\ \\ \bigstar \: \sf{ C.P =\dfrac{100}{100+Gain\%} \times S.P} \\ \\\bigstar \: \sf{ S.P = \dfrac{100-loss\%}{100} \times C.P} \\ \\ \bigstar \: \sf{ C.P =\dfrac{100}{100-loss\%} \times S.P}\end{array} }$