Question

A chair was sold for 1296 with a profit of 8%. What was the cost price
of the chair?
Step By Step.​

Answer 1

Given:

• Selling price (S.P.) of a Chair = ₹ 1296.

• Profit gained by selling = 8 %.

To find:

• The cost price (C.P.) of the Chair.

Understanding the concept:

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

• Cost Price (C.P.) - The price at which 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 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 solve the problem now!!

Formula to be used:

$\rm :\longmapsto\: \boxed{ \sf{Cost \: Price \: = \dfrac{100 \times Selling \: Price}{100 + profit\%} }}$

Solution:

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

$\rm :\longmapsto\:Cost \: Price \: = \dfrac{100 \times Selling Price}{100 + profit\%}$

We have,

• Selling Price of chair = ₹ 1296

• Profit % = 8 %

On substituting these values in the formula, we get

$\rm :\longmapsto\:Cost \: Price \: = \dfrac{1296 \times 100}{100 + 8}$

$\rm :\longmapsto\:Cost \: Price \: = \dfrac{129600}{108}$

$\bf\implies \:Cost \: Price \: = \: 1200$

Hence,

• Cost Price of Chair = ₹ 1200

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