Question

A dealer gain 7% by selling a sofa set for RS 3852 find his gain or loss percents. If he sells it for 4050.

Answer 1

$\Large{\textbf{\underline{\underline{According\:to\:the\:Question}}}}$

${\boxed{\sf\:{Gain\;or\;Profit}}}$

= 7%

${\boxed{\sf\:{Selling\;Price\;of\;Sofa}}}$

= 3852

${\boxed{\sf\:{Cost\;Price\;(Formula)}}}$

$\tt{\rightarrow\dfrac{100}{100+P}\times SP}$

${\boxed{\sf\:{Substitute\;the\;values\;we\;get:-}}}$

$\tt{\rightarrow\dfrac{100}{107}\times 3852}$

= 3600

${\boxed{\sf\:{Profit\;or\;Gain}}}$

$\textbf{\underline{Selling\;Price\;-\;Cost\;Price}}$

= 4050 - 3600

= 450

Now,

${\boxed{\sf\:{Profit\;or\;Gain\;Percentage}}}$

${\boxed{\sf\:{\dfrac{Gain}{CP}\times 100}}}$

$\tt{\rightarrow\dfrac{450}{3600}\times 100}$

$\tt{\rightarrow\dfrac{450}{36}}$

= 12.5%.

$\Large{\boxed{\sf\:{Hence\;Gain=12.5\;Percent}}}$

$\Large{\textbf{\underline{Additional\;Information}}}$

Situation

If SP is < than CP then loss :-

1] Profit = SP - CP

2] Selling price = CP + profit

3] Cost price = SP - profit

Answer 2

AnswEr :

⠀

The Gain% on Sofa will be 12.5% if he sells at Rs. 4050

⠀

Explanation :

• SP of Sofa = Rs. 3852

• Gain% = 7%

• We Need to Find Gain% or Loss% , if he sells at Rs. 4050.

◐ We Know the Formula :

$\large \boxed{ \bold{SP = CP \times \frac{(100 + gain\%)}{100} }}$

➟ 3852 = CP × $\large\bold{\frac{107}{100}}$

➟ 36 = CP × $\large\bold{\frac{1}{100}}$

➟ CP = 36 × 100

➟ CP = Rs. 3600

━━━━━━━━━━━━━━━━━━━━━━━━

• CP = Rs. 3600

• SP = Rs. 4050

» Gain = SP - CP

» Gain = Rs. (4050 - 3600)

» Gain = Rs. 450

$\large \boxed{ \bold{Gain\% = \frac{Gain}{CP} \times 100}}$

➟ Gain% = $\large\bold{\frac{450}{3600}}$ × 100

➟ Gain% = $\large\bold{\frac{450}{36}}$

➟ Gain% = 12.5%

⠀

$\large\therefore$ The Gain% will be 12.5%