Question

If a person sells a saree for Rs 2600 and makes a profit of 30%, then what was the cost price of the saree.
Pls give explanation aswell , I will mark you BRAINLIEST
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Answer 1

Given:

• Selling price (S.P.) of a saree = ₹2,600.
• Profit gained by selling = 30%.

To find:

• The cost price (C.P.) of the saree.

Understanding the concept:

‎ ‎ ‎ ‎ ‎ ‎We're given with the selling price and the profit gained by selling a saree. And we're asked to find the cost price of the saree. For finding this, first let's recall the chapter- "Profit and Loss", which we've studied in previous classes!

• Cost Price (C.P.) - The price at which an article is purchased is called it's cost price.
• Selling Price (S.P.) - The price at which an article is sold is called it's selling price.
• Profit - If the S.P. of an article is greater than its C.P., we say that there is a profit.
• Loss - If the S.P. of an article is less than its C.P., we say that there is a loss.
• Overheads - All the expenditure incurred on transportation, repairs, etc are categorised as overheads. Overheads are always included in the C.P. of the article.

In this question, we're only going to deal with the first three sub-topics which are mentioned above. Let's start calculating the required answer!

Formula to be used:

$\underline{\boxed{\bf{ C.P. = \bigg(\sf\dfrac{100}{100+Gain \: \% \: (or) \: Loss\:\%} \times S.P \bigg)}}}$

Solution:

As per the given data, we've all the required values to substitute them in the formula to find C.P.$\\ \longrightarrow\tt{ \pink{C.P. = \bigg(\dfrac{100}{100+Gain \: \% \: (or) \: Loss\:\%} \times S.P \bigg)}}$

• S.P. = 2600
• Profit % = 30

Now, on substituting these measures,

$\\ \longmapsto { \sf{C.P. = \dfrac{100}{100 + 30} \times 2600}} \\ \\ \longmapsto{ \sf{C.P. = \dfrac{100 \times 260 \cancel{0}}{13 \cancel{0}}}} \\ \\ \longmapsto{ \sf{C.P. \dfrac{ \cancel{26000}}{ \cancel{13}} }} \\ \\ \longmapsto \boxed{ \tt{ \pmb { \red{C.P. = 2,000}}}}$

We've obtained the C.P. as ₹2,000. Let's verify it!

Verification:

To verify, let's ignore the value of S.P. in the formula and insert the obtained C.P. and profit % in it. Then we shall check does the given value of S.P. equals the same that we get here.

$\\ \longmapsto { \sf{C.P. = \dfrac{100}{100 + profit \: \%} \times S.P.}} \\ \\ \longmapsto{ \sf{2000 = \dfrac{100}{100 + 30} \times S.P.}} \\ \\ \longmapsto{ \sf{2000 = \dfrac{100}{130} \times S.P. }} \\ \\ \longmapsto{ \sf{2000 \times 130 = 100 \times S.P.}} \\ \\ \longmapsto{ \sf{260000 = 100 \times S.P.}} \\ \\ \longmapsto{ \sf{ \frac{2600 \cancel{00}}{ 1\cancel{00}} = S.P. }} \\ \\ \longmapsto { \underline{ \underline{ \bf{2,600 = S.P.}}}}$

Since, the S.P. amount is same, our answer is correct!

$\\ \therefore\underline{\sf{\pmb{The\:Cost\: Price\:of\:the\:saree\:is\:\gray{2,000/-}.}}}$

___________________________________________

$\: \: \: \: \: \: \begin{gathered}\begin{gathered} \footnotesize{\boxed{ \begin{array}{cc} \small\underline{\frak{\pmb{ \red{More \: Formulae}}}} \\ \\ \bigstar \: \bf{Gain = \sf S.P. \: – \: C.P.} \\ \\ \bigstar \:\bf{Loss = \sf C.P. \: – \: S.P.} \\ \\ \bigstar \: \bf{Gain \: \% = \sf \Bigg( \dfrac{Gain}{C.P.} \times 100 \Bigg)\%} \\ \\ \bigstar \: \bf{Loss \: \% = \sf \Bigg( \dfrac{Loss}{C.P.} \times 100 \Bigg )\%} \\ \\ \\ \bigstar \: \bf{S.P. = \sf\dfrac{100+Gain \: \% \: (or) \: Loss\:\%}{100} \times C.P.} \\ \: \end{array} }}\end{gathered}\end{gathered}$

Answer 2

Selling price of a saree = ₹2600

Its profit = 30%

Cost price of the saree = ??

‎

By using formula: $C.P = \dfrac{100 \times S.P}{100+Profit \: \%}$

‎

Cost price:

⇛ (100 × 2600)/(100+30)

⇛ 26000/130

⇛ 2000/-

‎

Therefore, C.P of the saree is 2000/-