Question

The marked price of an article is 25% above it's selling price and the cost price is 30% less than its marked price . find the discount percentage and gain percent.​

Answer 1

Answer:

25%

Step-by-step explanation:

suppose selling price is x

Marked Price = 1.25 x

Cost Price = 1.25 x - .4(1.25x)= 1.25x- .5x

Cost Price = .75x

Selling Price = Cost Price + Profit

Profit = Selling price - Cost price

= x - 0.75x

=0.25x

Hence Profit is 25 %

Discount is 25 %

Answer 2

$\large\underline{\sf{Solution-}}$

According to given problem,

• The MP of an article is 25 % above the selling price and the cost price is 30% less than its MP.

• Let the Marked Price be = Rs 100

• Let Selling Price of an Article be Rs 'x'.

Since,

• The MP of an article is 25 % above the selling price.

$\sf :\implies\:x + 25\% \: of \: x = 100$

$\rm :\longmapsto\:x + \dfrac{25}{100} x = 100$

$\rm :\longmapsto\:x + \dfrac{x}{4} = 100$

$\rm :\longmapsto\:\dfrac{4x + x}{4} = 100$

$\rm :\longmapsto\:\dfrac{5x}{4} = 100$

$\rm :\implies\:x = 80$

So,

• Selling Price of an Article = Rs 80

Now,

• The cost price is 30% less than its MP.

$\rm :\implies\:Cost \: Price \: of \: an \: article \: = \: Rs \: 70$

Now, we have

• Marked Price of the Article = Rs 100

• Selling Price of an Article = Rs 80

• Cost Price of an Article = Rs 70

We know,

$\sf \: gain\% \: = \dfrac{Selling Price - Cost Price}{Cost Price} \times 100\%$

$\rm :\longmapsto\:gain\% \: = \: \dfrac{80 - 70}{70} \times 100\%$

$\rm :\longmapsto\:gain\% = \dfrac{10}{7} \times 10\%$

$\bf\implies \:gain\% = 14.28\%$

Also,

$\sf \: Discount\% = \dfrac{Marked Price - Selling Price}{Marked Price} \times 100\%$

$\rm :\longmapsto\:Discount\% = \dfrac{100 - 80}{100} \times 100\%$

$\bf :\implies\:Discount\% = \: 20\%$

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$\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \footnotesize{\boxed{ \begin{array}{cc} \small\underline{\frak{\pmb{ {More \: Formulae}}}} \\ \\ \bigstar \: \bf{Gain = \sf S.P. \: – \: C.P.} \\ \\ \bigstar \:\bf{Loss = \sf C.P. \: – \: S.P.} \\ \\ \bigstar \: \bf{Gain \: \% = \sf \Bigg( \dfrac{Gain}{C.P.} \times 100 \Bigg)\%} \\ \\ \bigstar \: \bf{Loss \: \% = \sf \Bigg( \dfrac{Loss}{C.P.} \times 100 \Bigg )\%} \\ \\ \\ \bigstar \: \bf{S.P. = \sf\dfrac{(100+Gain\%) \: (or) \: (100 - Loss\%)}{100} \times C.P.} \\ \: \end{array} }}\end{gathered}\end{gathered}\end{gathered}$