John goes to buy clothes in a shop where there is a discount of 30% on

Question

John goes to buy clothes in a shop where there is a discount of 30% on all items. Additionally there is an offer of " Buy 3 for 40% off" that is the discount increases to 40% on each item if he purchases 3 items. If John has already purchased two items priced $ 40 and $ 20, how much can he buy the third item for and still pay only what he was paying for the two items initially?
(A) $4
(B) $6
(C) $10
(D) $14
(E) $45

At the mall - in same situation

JeffTargetTestPrep · Accepted Answer

Note that when an item is discounted by, say, 40%, we are paying 60% (or 0.6) of its original price. 
Similarly, when an item is discounted by 30%, we are paying 70% (or 0.7) of its original price. With this in mind, and letting x = the regular price of the third item, we can create the following equation:

0.6(40 + 20 + x) = 0.7(40 + 20)

24 + 12 + 0.6x = 28 + 14

0.6x = 6

x = 6/0.6 = 60/6 = 10

Answer: C

chetan2u · Answer

It is a great feeling to realize that you picked up the third item absolutely free

. reserved for OE.. Two ways... 1) items at 30% discount will become at 40%, so an addl profit of 10%. 10% of (20+40)=$6 So this should be the price you pay for 3rd item after discount .. Since the item is at 40% discount, you pay 60% So 60% = 6 100% will be 6*100/60=10 2) price of third item =x.. The price of 3 items at 40% discount = the price of two items at 30% So 0.6(40+20+x)=0.7(40+20)....... 360+6x=420......6x=420-360=60......x=10

sunita123 · Answer

Let $x is the price of 3rd item
40% discount on 3 items means he has to pay 60% of the total price
he was paying $42 initially that is is 30% discount of $40 +$20
so equation becomes 
.6($40+$20+x)=$42 
by solving , x= $10
Ans C

MikeScarn · Answer

I would say it depends on how you interpret the question. The situation is not clear. Has John purchased two items for $40 and $20  after  the 30% off? Or is that not including the 30% off?

Since the first sentence clearly states that there is a discount of 30% on all items, I would say that the $40 and $20 is the price  after  the discount.

That being said, you can calculate the non-discounted price of each item by doing  \frac{20}{.7}  = 28 and  \frac{40}{.7}  = 57.

Now to find the price of the third item 0.6(57+28+x)=60

x=14.

Answer: D

chetan2u · Answer

Thanks. edited to remove ambiguity

nihilveritatis · Answer

I think the final wording is a little ambiguous - the question asks how much can he buy the third item for?

That is 6$, the full price of this item is 10 but he can buy it for 6$ while spending the same as before.

10$ would be the right answer if it was worded in a way that asked for the value of the third item rather than what he paid for it

HouseOfStone · Answer

I also interpreted it like this. The item costs $10 but he can purchase it for $6 at the discount. I view original price vs purchase price different

John goes to buy clothes in a shop where there is a discount of 30% on

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John goes to buy clothes in a shop where there is a discount of 30% on

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