Question

Q 75. The marked price of an article is 20% higher than its cost price. Then the percentage of profit gained after allowing an
discount of 6.25% is
Oa) 21%
Ob) 15%
Oc) 18%
Od) 12.5%​

Answer 1

Answer:

• The percentage of profit gained after allowing an discount of 6.25% is 12.5%

Given:

• The marked price of an article is 20% higher than its cost price.

To find:

• Then the percentage of profit gained after allowing an discount of 6.25% is?

Solution:

Let the CP be Rs. 100

Then MP will be 100 + 20 = Rs. 120

Discount = 6.25% = $\bf \dfrac{6.25}{100} \times 120$

➥ $\bf \dfrac{6.25}{10} \times 12$

➥ $\bf \dfrac{6.25}{100} \times 120$

➥ 0.00625 × 120

➥ Rs. 7.5

We know that,

SP = MP - Discount %

➥ 120 - 7.5

➥ 112.5

Profit = SP - CP

➥ 112.5 - 100

➥ Rs. 12.5

Profit % = $\bf \dfrac{12.5}{100} \times 100$

➥ Profit % = 12.5 %

Answer 2

Correct Question-:

• The marked price of an article is 20% higher than its cost price. Then the percentage of profit gained after allowing an discount of 6.25% is ___________.

AnswEr -:

• $\underline{\boxed{\star{\sf{\blue{  \:The\: percentage\: of \:profit\: gained \:after\: allowing\: an\:discount\: of \:6.25\%\:= 12.5\%}}}}}$
• $\underline{\boxed{\star{\sf{\blue{  \:The\: Option (D)\:or\: 12.5\%\:is\:correct\:.}}}}}$

EXPLANATION-:

• $\frak{Given \:\: -:} \begin{cases} \sf{The \:marked\: price\: of \:an\: article \:is \:20\%\: higher\: than \:its\: cost \:price} & \\\\ \sf{ The\:discount \: \:given\:is\:of\:6.25 \%}\end{cases}$
• $\frak{To \:Find\: -:} \begin{cases} \sf{ The\: percentage\: of \:profit\: gained \:after\: allowing\: an\:discount\: of \:6.25 \%}\end{cases}$

Solution-:

• Let the Cost Price or C.P be Rs.100
• Then ,
• The marked price of an article is 20% higher than its cost price.
• $\implies{\sf{\large {Marked \: Price = 100 + 20\% of 100 }}}$
• $\implies{\sf{\large {Marked \: Price = 100 + \frac {20}{100} × 100 }}}$
• $\implies{\sf{\large {Marked \: Price = 100 + 20 }}}$
• $\implies{\sf{\large {Marked \: Price = Rs.120 }}}$

$\underline{\boxed{\star{\sf{\blue{  Marked \:Price= Rs.120.}}}}}$

Now ,

• Discount Given of 6.25% on Marked Price = Rs.120
• $\implies{\sf{\large {Discount \: Price = 6.25\% of 120 }}}$
• $\implies{\sf{\large {Discount \: Price = \frac{6.25}{100} × 120 }}}$
• $\implies{\sf{\large {Discount \: Price = \frac{6.25}{10} × 12 }}}$
• $\implies{\sf{\large {Discount \: Price = 0.625 × 12 }}}$
• $\implies{\sf{\large {Discount \: Price = Rs.7.5 }}}$

$\underline{\boxed{\star{\sf{\blue{  Discount\:Price= Rs.7.5.}}}}}$

We know That ,

• $\underline{\boxed{\star{\sf{\blue{  Selling \:Price= Marked\:Price - \: Discount.}}}}}$
• Here -:
• Marked Price = Rs.120
• Discount Price = Rs.7.5

Now ,

• $\implies{\sf{\large {Selling \: Price = 120 - 7.5 }}}$
• $\implies{\sf{\large {Selling \: Price = 112.5 }}}$

Now ,

• $\underline{\boxed{\star{\sf{\blue{  Profit \:= Selling \:Price - \: Cost\:Price.}}}}}$
• Here ,
• Selling Price = Rs . 112.5
• Cost Price = Rs . 100

Now ,

• $\implies{\sf{\large { \: Profit = 112.5 - 100 }}}$
• $\implies{\sf{\large { \: Profit = Rs.12.5 }}}$

$\underline{\boxed{\star{\sf{\blue{  \:Profit= Rs.12.5.}}}}}$

Then ,

• $\underline{\boxed{\star{\sf{\blue{  Profit \:\%= \frac {Profit× 100}{Cost\: Price}.}}}}}$
• Here ,
• Profit = Rs.12.5
• Cost Price = Rs.100

Now ,

• $\implies{\sf{\large {Profit \: Percentage = \frac{12.5×100}{100} }}}$
• $\implies{\sf{\large {Profit \: Percentage = 12.5\% }}}$

Therefore,

• $\underline{\boxed{\star{\sf{\blue{  \:Profit\: Percentage\:= 12.5\%.}}}}}$

Hence,

• $\underline{\boxed{\star{\sf{\blue{  \:The\: percentage\: of \:profit\: gained \:after\: allowing\: an\:discount\: of \:6.25\%\:= 12.5\%.}}}}}$
• $\underline{\boxed{\star{\sf{\blue{  \:The\: Option (D)\:or\: 12.5\%\:is\:correct\:.}}}}}$

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