Question

20% more can be gained if a piece of cloth is sold for 83rs instead of 78rs. find the cost price of piece of cloth.

Answer 1

Let the cost price = x

let the gain when it is sod at Rs 78 is y%.Thus 

$\frac{78-x}{x} \times 100=y\\ \\ \Rightarrow \frac{100(78-x)}{x}=y\\ \\ \Rightarrow y = \frac{7800-100x}{x}$

When it is sold at Rs. 83, gain is 20% more or gain is (y+20)%.Thus
$\frac{83-x}{x} \times 100=y+20\\ \\ \Rightarrow \frac{100(83-x)}{x}=y+20\\ \\ \Rightarrow y+20 = \frac{8300-100x}{x}\\ \\ \Rightarrow \frac{7800-100x}{x}+20 = \frac{8300-100x}{x}\\ \\ \Rightarrow \frac{7800-100x+20x}{x} = \frac{8300-100x}{x}\\ \\ \Rightarrow \frac{7800-80x}{x} = \frac{8300-100x}{x}\\ \\ \Rightarrow 7800-80x= 8300-100x\\ \\ \Rightarrow 100x-80x= 8300-7800\\ \\ \Rightarrow 20x=500\\ \\ \Rightarrow x= \frac{500}{20}=Rs. 25$

So the cost price is Rs. 25.

============================================
Alternatively:

Let cost price = x
When the cloth is sold at Rs 83 instead of Rs 78,
more gain = 83 - 78 = Rs. 5
given that more gain = 20%.

$\frac{5}{x} \times 100 = 20\\ \\ \Rightarrow \frac{500}{x}=20 \\ \\ \Rightarrow x = \frac{500}{20}=Rs.\ 25$

So Cost price is Rs. 25

Answer 2

Answer:

Rs. 25

Step-by-step explanation:

Let the cost price = x

let the gain when it is sod at Rs 78 is y%.Thus

\begin{gathered}\frac{78-x}{x} \times 100=y\\ \\ \Rightarrow \frac{100(78-x)}{x}=y\\ \\ \Rightarrow y = \frac{7800-100x}{x}\end{gathered}

x

78−x

×100=y

⇒

x

100(78−x)

=y

⇒y=

x

7800−100x

When it is sold at Rs. 83, gain is 20% more or gain is (y+20)%.Thus

\begin{gathered}\frac{83-x}{x} \times 100=y+20\\ \\ \Rightarrow \frac{100(83-x)}{x}=y+20\\ \\ \Rightarrow y+20 = \frac{8300-100x}{x}\\ \\ \Rightarrow \frac{7800-100x}{x}+20 = \frac{8300-100x}{x}\\ \\ \Rightarrow \frac{7800-100x+20x}{x} = \frac{8300-100x}{x}\\ \\ \Rightarrow \frac{7800-80x}{x} = \frac{8300-100x}{x}\\ \\ \Rightarrow 7800-80x= 8300-100x\\ \\ \Rightarrow 100x-80x= 8300-7800\\ \\ \Rightarrow 20x=500\\ \\ \Rightarrow x= \frac{500}{20}=Rs. 25\end{gathered}

x

83−x

×100=y+20

⇒

x

100(83−x)

=y+20

⇒y+20=

x

8300−100x

⇒

x

7800−100x

+20=

x

8300−100x

⇒

x

7800−100x+20x

=

x

8300−100x

⇒

x

7800−80x

=

x

8300−100x

⇒7800−80x=8300−100x

⇒100x−80x=8300−7800

⇒20x=500

⇒x=

20

500

=Rs.25

So the cost price is Rs. 25.

============================================

Alternatively:

Let cost price = x

When the cloth is sold at Rs 83 instead of Rs 78,

more gain = 83 - 78 = Rs. 5

given that more gain = 20%.

\begin{gathered}\frac{5}{x} \times 100 = 20\\ \\ \Rightarrow \frac{500}{x}=20 \\ \\ \Rightarrow x = \frac{500}{20}=Rs.\ 25\end{gathered}

x

5

×100=20

⇒

x

500

=20

⇒x=

20

500

=Rs. 25

So Cost price is Rs. 25