Question

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the CP. of 6 articles is equal to the S.P. of 4 articles find the gain per cent.​

Answer 1

Answer :-

The gain percentage is 50 %.

Solution :-

Let the CP of one article be x

CP of 6 articles = 6 * x = 6x

CP of 4 articles = 4 * x = 4x

$\bf \bigstar\: SP = CP \times \bigg(\dfrac{100 + g \%}{100} \bigg) \\ \\ \sf SP\:of\:4 \: articles = 4x \bigg( \dfrac{100 + g}{100} \bigg)$

Given

CP of 6 articles = SP of 4 articles

$\sf \implies 6x = 4x \bigg( \dfrac{100 + g}{100} \bigg)$

Cancelling x on both sides

$\sf \implies 6 = 4 \bigg( \dfrac{100 + g}{100} \bigg) \\ \\ \sf \implies 6 \times 100 = 4(100 + g) \\ \\ \sf \implies 600 = 400 + 4g \\ \\ \sf \implies 600 - 400 = 4g \\ \\ \sf \implies 200 = 4g \\ \\ \sf \implies \dfrac{200}{4} = g \\ \\ \sf \implies g = 50 \\ \\ \sf \implies g \% = 50 \%$

Therefore the gain percentage is 50 %.

Answer 2

Answer :

The gain percentage is 50%.

Step-by-step explanation :

Given that :

The C.P of 6 articles is equal to the S.P. of 4 articles.

To Find :

The gain percentage.

Solution :

$\bigstar\;\textbf{\underline{\underline{Consider as -}}}}$

Cost Price of 1 article as - Rs. 1.

Cost Price of 6 articles as - Rs. 6.

Also,

The S.P of 4 articles = Rs. 6

The S.P of 1 article = $\sf \dfrac{6}{4}$

Now,

$\sf \\ \\\implies \dfrac{6}{4} > \dfrac{1}{1}\\ \\\implies \therefore SP > CP\quad(It\;is\;Gain)\\ \\\implies Gain = \dfrac{6}{4} - \dfrac{1}{1}\\ \\\implies \dfrac{6-4}{4}\\ \\\implies \dfrac{2}{4}$

We know that :

$\bigstar\;\boxed{\sf {Gain\% =\dfrac{Gain}{C.P}\times 100}}}\\ \\ \\\bf{\underline{{Put\;the\;values:}}}\\ \\ \\\implies \dfrac{2}{4}\;\div \dfrac{1}{1} \times 100.\\ \\ \\\implies \dfrac{2}{4} \times \dfrac{1}{1} \times 100. \\ \\ \\\implies 50\%.\\ \\ \\ \\\bigstar\;\textbf{\underline{\underline{The gain percentage is 50\%.}}}$