Question

a dealer purchased a fan for rs.1080. after allowing a discount of 25% on its marked price, he gains 25%. find the marked price of the fan.​

Answer 1

Answer -

Given :-

• CP = Rs. 1080
• Profit percentage = 25 %
• Discount percentage = 25 %

To Find :-

• Marked price, MP

Formula used :-

$\boxed{\sf SP = \frac{100+P\%}{100} \times CP}$

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$\boxed{\sf MP = \frac{100}{100-D\%} \times SP}$

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Solution :-

To find the marked price, we first need to find selling price -

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Calculating Selling price :-

$\sf SP = \frac{100+P\%}{100} \times CP$

Substituting the values -

➩ $\sf SP = \frac{100+ 25}{100} \times 1080$

➩ $\sf SP = \frac{125}{10 \cancel0}\times 108\cancel0$

➩ $\sf SP = \frac{\cancel{12}5}{\cancel{10}} \times \cancel{10}8$

➩ $\sf SP = 1350$

Selling price, SP = Rs. 1350

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Calculating marked price :-

We have,

• D = 25%
• SP = Rs. 1350

Substituting the values :-

➩ $\sf MP = \frac{100}{100-D\%} \times SP$

➩ $\sf MP = \frac{100}{100-25} \times 1350$

➩ $\sf MP = \frac{100}{75} \times 1350$

➩ $\sf MP = 1800$

Hence, marked price of fan is ₹ 1800.

Answer 2

★ Given :

• Cost price (CP) = ₹ 1080
• Discount on it's marked price = 25%
• He Gains = 25%

★ To Find :

• Market price of a fan ?

★ Solution :

◆ We know that,

↦ Selling price = 100 + gain% / 100 × Cp

Now, Substitute the values :-

↦ 100 + 25 / 100 × 1080

↦ 125 / 100 × 1080

↦ 1.25 × 1080

↦ ₹ 1350

■ Hence, the selling price is ₹ 1350.

◆ We also know that,

☯︎ Let the Market price be 'x'

↦ Market price = ( Sp × 100 ) / ( 100 - Discount )

Now, Substitute the values :-

↦ X = ( 1350 × 100 ) / ( 100 - 25 )

↦X = 135000 / 75

↦X = ₹ 1800

■ Hence, the Market price of a fan is ₹ 1800.