Question

by selling an article for Rs. 480, the shopkeeper loses 20%.Find the gain or loss per cent if the article is sold for Rs. 660​

Answer 1

$\mathfrak{\large{\underline{\underline{Answer:}}}}$

The Gain % when the article is sold for Rs. 660 is 10%.

$\mathfrak{\large{\underline{\underline{Step-by-step\: explanation}}}}$

$\textsf{\underline{\underline{Given : }}}$

Selling the article at = Rs. 480

Loss occurred = 20%

$\textsf{\underline{\underline{To find :}}}$

Gain or loss when the article is sold for Rs. 660.

$\textsf{\underline{\underline{Solution :}}}$

$\textbf{Case I -}$

Here :

• Selling Price = Rs. 480
• Loss = 20%
• Cost Price = ??

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

$\longrightarrow{\sf\:{CP = \frac{100}{(100 - loss\%)} \times SP}} \\ \\ \longrightarrow{\sf\:{CP = \frac{100}{(100 - 20)} \times 480}} \\ \\ \longrightarrow{\sf\:{CP = \frac{100}{80} \times 480}} \\ \\ \longrightarrow{\sf\:{CP = \frac{48000}{80}}} \\ \\ \longrightarrow{\sf\:{CP = 600}}$

Cost Price of the article is Rs. 600.

$\rule{300}{1.5}$

$\textbf{Case II -}$

Here :

• Cost Price = Rs. 600 (from above calculations)
• Selling Price = Rs. 660
• Loss or Gain % = ??

660 > 600

Selling Price > Cost Price

$\therefore$ It's a Gain !

$\bigstar{\green{\boxed{\green{\boxed{\red{\sf{{Gain\% = \frac{SP - CP}{CP} \times 100}}}}}}}}$

$\sf{\longrightarrow} \: {Gain\% = \frac{SP - CP}{CP} \times 100} \\ \\ \sf{\longrightarrow} \: {Gain\% = \frac{660 - 600}{600} \times 100} \\ \\ \sf{\longrightarrow} \: {Gain\% = \frac{60}{600} \times 100 }\\ \\ \sf{\longrightarrow} \: {Gain\% = \frac{6000}{600}} \\ \\ \sf{\longrightarrow} \: {Gain\% = 10\%}$

Gain % = 10%

$\therefore$ The Gain % when the article is sold for Rs. 660 is 10%.

Answer 2

Answer :-

Gain % is 10 %

Explanation :-

Finding Cost price of an article when he loses 20 %

Selling price of an article (SP) = Rs. 480

Loss % (l) = 20 %

Cost price (CP) = (SP * 100)/(100 - l)

= (480 * 100)/(100 - 20)

= 48000/80

= 600

i.e CP of an article (CP) = Rs. 600

Finding gain or loss % when Selling price is Rs. 660

Cost price of an article (CP) = Rs. 600

Selling price of an article (SP) = Rs. 660

Here

SP > CP

So it is a Gain

Gain = SP - CP = 660 - 600 = Rs. 60

Gain % = (Gain/CP) * 100

= (60/600) * 100

= (6/6) * 10

= 1 * 10

= 10 %

i.e Gain % = 10 %

∴ Gain % is 10 %