Bill made a profit of 10% by selling a product. If he had purchased

Question

Bill made a profit of 10% by selling a product. If he had purchased that product for 10% less and sold it at a profit of 30%, he would have received $ 49 more. What was his original selling price?

(A) $770

(B) $660

(C) $700

(D) $1100

(E) $840

Source : Aristotle Prep

sagar2911 · Accepted Answer

Let the original purchase price be X
So original selling price at 10% profit = 1.1X

If product is purchased at 10% less of original = 0.9X
Profit of 30% on this price = 1.3(0.9X)

He would have received $49 more in second scenario => 1.3(0.9X) - 1.1X = 49
=> 0.07X = 49
=> X = $700

Original purchase price = $700
Hence, original selling price (at 10% of profit) = 1.1(700) = $770

Option A

ENGRTOMBA2018 · Answer

Let P be the original purchase price of Bill. Selling price for Bill originally = 1.1*P

Scenario 2, 10% less purchase price ---> 0.9*P, he would have made 30% profit. Thus selling price for this case = 1.3*0.9*P = 1.17*P

Thus, per the question, 1.17P-1.1P = 49 ---> P = 700

Finally, selling price for case 1 = 700*1.1 = 770. A is the correct answer.

HolaMaven · Answer

Lets use options.
 Option A:770 
Original SP = 770
Original CP =  \frac{770}{1.1}  = 700
New CP = 700-10%*700=630
New Profit = 30%*630 = 63*3 = 189
New SP = 189+630 = 819
New SP-Original SP = 819-770 = 49 , matching condition given in question.
 Thus answer is Option A 
 No need to work on remaining options

GmaticManish · Answer

Hi,
I am not so sure if my solution is really correct, but however I did come up with right answer with this method.

Since we are dealing with percentages here I just assumed
Let Original CP= 100
Now since Profit=10%. Original SP=110
The question says if the CP is 10% Lower, so now
New CP=90
,Then New SP=1.3*90=117 (Since sold at a profit of 30%)

Now Difference between Original SP and New SP= 117-110= 7
In the question it says that this difference is $ 49 which is 7*7.
Now if I just do 7*Original SP= 7*110 = 770, which is the answer.

Please let me know if its a correct approach, or if I just got lucky. Thanks

devdattakhoche · Answer

let's solve this problem assuming the original cost price (CP) is $100x$.

Original CP = $100x$
Profit = 10%
Original selling price (SP) = CP + 10% of CP = $100x + 0.10(100x) = 100x + 10x = 110x$

New CP = Original CP - 10% of Original CP = $100x - 0.10(100x) = 100x - 10x = 90x$
New Profit = 30%
New SP = New CP + 30% of New CP = $90x + 0.30(90x) = 90x + 27x = 117x$

We are given that the new selling price is $49 more than the original selling price.
So, New SP = Original SP + $49
$117x = 110x + 49$
$117x - 110x = 49$
$7x = 49$
$x = \frac{49}{7} = 7$

Original CP = $100x = 100(7) = 700$
Original SP = $110x = 110(7) = 770$

Therefore, the original selling price was $770.

Final Answer: The final answer is $\boxed{770}$

Bill made a profit of 10% by selling a product. If he had purchased

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