Question

if the costpirce of 55 items is equal to the selling prce of 50 itrms determine the gain in percentage
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Answer 1

Answer:

Let C.P of one article =1 Rs.

Then C.P of 40 article=40 Rs.

According to the question

S.P of 50 article =C.P of 40 article=40 Rs.

We assume that C.P of one article =1Rs.

then C.P of 50 article=50 Rs.

Loss=50-40=10 Rs.

Loss %=

50

10

×100=20%

Step-by-step explanation:

Its similar to your question

Answer 2

Answer:

$\bigstar\:\:{\Large\red{Gain\%\:=\:10\%}}$

Step-by-step explanation:

$\rm\large\green{\underline{Given:-}}$

• Cost Price (C.P) of 55 items and Selling Price (S.P) of 50 items is equal.

$\rm\large\green{To\:Find:-}$

• Gain = ?
• Gain% = ?

$\rm\Large\blue{\underline{Explanation:}}$

Let's the total price of 55 items and total selling price of 50 items be 'X'.

$\rm\large\green{\underline{Then,}}$

$\rightarrow \: c.p \: of \: 1 \: item \: = \dfrac{x}{55} \\ \\ \rightarrow \: s.p \: of \: 1 \: item \: = \dfrac{x}{50}$

$\rm\large\green{\underline{We\:Know,}}$

$\star\boxed{\blue{Gain=S.P-C.P}}$

$\rightarrow\rm{S.P-C.P(of\:one\:item)}$

$= \dfrac{x}{50} - \dfrac{x}{55} \\ \\ = 11x - \frac{10x}{550} \\ \\ = \frac{x}{550} \: \: \: \: \: \: \: \: \: \: \: \:$

$\frac{furmula}{\blue{ \bigstar\boxed{Gain\%= \frac{Gain}{C.P} \times 100}}}$

$= \dfrac{x}{550}^{(gain)} \div \dfrac{x}{55}^{(c.p)} \times 100$

$= \cancel{\dfrac{x}{550} \times \dfrac{55}{x} \times 100}^{10}\\ \\ \bf \: =\:10\% \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\bigstar\boxed{\Large\red{Therefore,\:Gain\%\:is\:10\%}}$

_________________________

$\Large\mathcal\red{Furmulae:-}$

$\bigstar\boxed{\blue{Gain=S.P-C.P}}$

${ \bigstar\boxed{\blue{Gain\%= \frac{Gain}{C.P} \times 100}}}$

$\bigstar\boxed{\blue{Loss=C.P-S.P}}$

${ \bigstar\boxed{\blue{Loss\%= \frac{Loss}{C.P} \times 100}}}$

$\bigstar\boxed{\blue{S.P=Gain+C.P}}$

$\bigstar\boxed{\blue{C.P=S.P-Gain}}$

$\bigstar\boxed{\blue{S.P=C.P-Loss}}$

$\bigstar\boxed{\blue{C.P=Loss+S.P}}$

_________________________

$\Large\rm\red{Difination:-}$

☯️ The buying price of any item is known as its Cost Price (C.P).

☯️ The price at which you sell is known as the selling price (S.P).