Question

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Q] A shopkeeper sells article at ₹45 per article giving 10% discount and earns 50% profit. If the discount is not given, then the profit gained is.


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Answer 1

Given :-

• SP = Rs.45
• Discount = 10%
• Profit = 50% .

To Find :-

• If the discount is not given, then the profit gained is. ?

Solution :-

Lets Solve with Basic First :-

→ SP = 45

→ D % = 10%

→ MP = (SP * 100) / (100 - D%)

→ MP = (45 * 100) / (100 - 10)

→ MP = ( 45 * 100) / 90

→ MP = Rs.50

Also,

→ SP = 45

→ Gain% = 50%

→ CP = (SP * 100) / (100 + P%)

→ CP = (45 * 100 / (100 + 50)

→ CP = (45 * 100) / (150)

→ CP = Rs.30

______________

Now it has been said that, when no discount is given, that means the article is sold at Marked price .

So,

→ SP = Rs.50

→ CP = Rs.30

→ Gain = SP - CP

→ Gain = 50 - 30

→ Gain = Rs.20

And,

→ Gain% = (Gain in Rs. * 100) / CP

→ Gain% = (20 * 100) / 30

→ Gain% = (2000/30)

→ Gain% = (200/3)

→ Gain% = 66.67% .

Hence, if No Discount is given the shopkeeper has overall gain of 66.67% .

_______________________

Now Lets Try with Direct Formula Also :-

☛ New Profit % = [ { (100 + P%) ( 100 - D₂) } / ( 100 - D₁) ] - 100%

we have :-

☞ P% = 50%

☞ D₁% = 10%

☞ D₂% = 0% { No Discount } .

So, Putting value we get :-

☛ New Profit = [ { (100 + 50) * (100 - 0) } / (100 - 10% ) ] - 100%

☛ New Profit = [(150 * 100) / 90] - 100%

☛ New Profit = 166.67% - 100%

☛ New Profit = 66.67% .

Hence, Profit In New case will be 66.67% .

________________________

[ Note :- we can solve it By Assuming CP as Rs. Also ].

Answer 2

Profit Gain - Rs. 20

Profit Gain % - 66.7 %

Step by step Explanation :

Given :

A shopkeeper sells article at ₹45 per article.

& offering 10% discount and earns 50% profit.

To find :

Profit.

Solution :

Let the C.P be Rs.100.

So,

Profit : 50 %

S.P :

=> 100 + 50

=> Rs. 150. [S.P]

Now, After Discount :

Sale price of Rs. 45

The CP would be =

$\implies \sf \dfrac{100}{150} \times 45$

$\implies \sf Rs.30$

If no discount was given :

The sale price will be :

=> 45/(1 - 10/100)

=> Rs. 50

So without discount,

The Sale Price is Rs. 50

The Cost Price is Rs.30.

We know that :

$\bigstar \: \boxed{ \bf \: Profit = SP - CP}$

Hence,

Profit = 50 - 30 = Rs. 20

Profit % =

$\implies \sf\dfrac{20}{30} \times 100$

$\implies \sf \: 66.67 \%$