Question

a man sold two gas stoves for rupees 8400 each.it is sold one at a gain of 20% and the other at a loss of 20% find his gain or loss percentage in the whole transaction​

Answer 1

Answer:

It is a Loss of 4%.

Step-by-step explanation:

Given :

Sold the gas stoves at = Rs. 8400 each.

Gain % on one = 20%

Loss % on another = 20%

To find :

The Gain or Loss % of the whole transaction.

Solution :

$\textsf{\underline{\underline{Case I -}}}$

Here :

• Selling Price = Rs. 8400
• Gain = 20%
• Cost Price = ??

$\bigstar{\boxed{\sf\:{CP = \frac{100}{(100 + Profit\%)} \times SP}}}$

$\sf{\longrightarrow} \: CP = \dfrac{100}{(100 + 20\%)} \times 8400 \\ \\ \sf{\longrightarrow} \: CP = \dfrac{100}{120} \times 8400 \\ \\ \sf{\longrightarrow}\: CP = \dfrac{840000}{120} \\ \\ \sf{\longrightarrow}\: CP = 7000$

Cost Price of the first stove is Rs. 7000.

$\rule{300}{1.5}$

$\textsf{\underline{\underline{Case II -}}}$

Here :

• Selling Price = Rs. 8400
• Loss % = 20%
• Cost Price = ??

$\bigstar \: {\boxed{\sf\:{CP = \frac{100}{(100 - loss\%)} \times SP}}}$

$\sf{\longrightarrow} \: CP = \dfrac{100}{(100 - 20\%)} \times 8400 \\ \\ \sf{\longrightarrow} \: CP = \dfrac{100}{80} \times 8400 \\ \\ \sf{\longrightarrow} \: CP = \dfrac{840000}{80} \\ \\ \sf{\longrightarrow} \: CP = 10500$

Cost Price of the second stove = Rs. 10,500

$\rule{300}{1.5}$

$\textbf{Total Loss or Gain \% =}$

✯ $\textsf{Total Cost Price = }$

$\sf{\longrightarrow} \: 7000 + 10500 \\ \\ \sf{\longrightarrow} \: 17500$

✯ $\textsf{Total Selling Price =}$

$\sf{\longrightarrow} \: 8400 + 8400 \\ \\ \sf{\longrightarrow} \:16800$

17,500 > 16800

SP > CP

$\therefore$ It is a Loss !

$\rule{300}{1.5}$

$\textsf{\underline{\underline{Loss -}}}$

★ $\boxed{\sf{Cost\: Price-Selling\: Price}}$

$\sf{\longrightarrow}\: 17500 - 16800 \\ \\\sf{\longrightarrow}\: 700$

Loss = Rs. 700

$\rule{300}{1.5}$

$\textsf{\underline{\underline{Loss \% - }}}$

$\bigstar\:{\boxed{\sf\:{Loss\% = \frac{CP - SP}{CP} \times 100}}}$

$\sf{\longrightarrow}\:Loss\% = \dfrac{700}{17500} \times 100 \\ \\ \sf{\longrightarrow}\:Loss\% = \dfrac{70000}{17500} \\ \\ \sf{\longrightarrow}\:Loss\% = 4\%$

Loss % = 4%

$\therefore$ It is a Loss of 4%.

Answer 2

Answer:

Answer:

It is a Loss of 4%.

Step-by-step explanation:

Given :

Sold the gas stoves at = Rs. 8400 each.

Gain % on one = 20%

Loss % on another = 20%

To find :

The Gain or Loss % of the whole transaction.

Solution :

\textsf{\underline{\underline{Case I -}}}Case I -

Here :

Selling Price = Rs. 8400Gain = 20%Cost Price = ??

\bigstar{\boxed{\sf\:{CP = \frac{100}{(100 + Profit\%)} \times SP}}}★CP=(100+Profit%)100×SP

\begin{gathered}\sf{\longrightarrow} \: CP = \dfrac{100}{(100 + 20\%)} \times 8400 \\ \\ \sf{\longrightarrow} \: CP = \dfrac{100}{120} \times 8400 \\ \\ \sf{\longrightarrow}\: CP = \dfrac{840000}{120} \\ \\ \sf{\longrightarrow}\: CP = 7000\end{gathered}⟶CP=(100+20%)100×8400⟶CP=120100×8400⟶CP=120840000⟶CP=7000

Cost Price of the first stove is Rs. 7000.

\rule{300}{1.5}

\textsf{\underline{\underline{Case II -}}}Case II -

Here :

Selling Price = Rs. 8400Loss % = 20%Cost Price = ??

\bigstar \: {\boxed{\sf\:{CP = \frac{100}{(100 - loss\%)} \times SP}}}★CP=(100−loss%)100×SP

\begin{gathered}\sf{\longrightarrow} \: CP = \dfrac{100}{(100 - 20\%)} \times 8400 \\ \\ \sf{\longrightarrow} \: CP = \dfrac{100}{80} \times 8400 \\ \\ \sf{\longrightarrow} \: CP = \dfrac{840000}{80} \\ \\ \sf{\longrightarrow} \: CP = 10500\end{gathered}⟶CP=(100−20%)100×8400⟶CP=80100×8400⟶CP=80840000⟶CP=10500

Cost Price of the second stove = Rs. 10,500

\rule{300}{1.5}

\textbf{Total Loss or Gain \% =}Total Loss or Gain % =

✯ \textsf{Total Cost Price = }Total Cost Price = 

\begin{gathered}\sf{\longrightarrow} \: 7000 + 10500 \\ \\ \sf{\longrightarrow} \: 17500\end{gathered}⟶7000+10500⟶17500

✯ \textsf{Total Selling Price =}Total Selling Price =

\begin{gathered}\sf{\longrightarrow} \: 8400 + 8400 \\ \\ \sf{\longrightarrow} \:16800\end{gathered}⟶8400+8400⟶16800

17,500 > 16800

SP > CP

\therefore∴ It is a Loss !

\rule{300}{1.5}

\textsf{\underline{\underline{Loss -}}}Loss -

★ \boxed{\sf{Cost\: Price-Selling\: Price}}CostPrice−SellingPrice

\begin{gathered}\sf{\longrightarrow}\: 17500 - 16800 \\ \\\sf{\longrightarrow}\: 700\end{gathered}⟶17500−16800⟶700

Loss = Rs. 700

\rule{300}{1.5}

\textsf{\underline{\underline{Loss \% - }}}Loss % - 

\bigstar\:{\boxed{\sf\:{Loss\% = \frac{CP - SP}{CP} \times 100}}}★Loss%=CPCP−SP×100

\begin{gathered}\sf{\longrightarrow}\:Loss\% = \dfrac{700}{17500} \times 100 \\ \\ \sf{\longrightarrow}\:Loss\% = \dfrac{70000}{17500} \\ \\ \sf{\longrightarrow}\:Loss\% = 4\%\end{gathered}⟶Loss%=17500700