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.

Answer 1

Answer:

2000rs

Step-by-step explanation:

s.p 130%=2600

c.p 100%=2000

Answer 2

Answer:

$\small\underline{\frak{\pmb{ \red{ Given : }}}}$

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

$\small\underline{\frak{\pmb{ \red{ To find : }}}}$

• 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.good
• 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!

$\small\underline{\frak{\pmb{ \red{ Formula \: to \: be \: used:- }}}}$

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

$\small\underline{\frak{\pmb{ \red{ Solution: }}}}$

As per the given data, we've all the required values to substitute them in the formula to find

$\begin{gathered} \\ \longrightarrow\tt{ \pink{C.P. = \bigg(\dfrac{100}{100+Gain \: \% \: (or) \: Loss\:\%} \times S.P \bigg)}}\end{gathered}$

S.P. = 2600

Profit % = 30

Now, on substituting these measures,

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

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

$\small\underline{\frak{\pmb{ \red{ Verification: }}}}$

• 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.

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

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

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

_________________________________________

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