Vicente bought two T-shirts for the same price. One had been

Question

Vicente bought two T-shirts for the same price. One had been marked down by 75%. If he had bought the two T-shirts for their regular prices, he would have paid three times as much. By what percent had the other T-shirt been marked down?

(A) 50%
(B) 58 \(\frac{1}{3}\)%
(C) 60%
(D) 62 \(\frac{1}{2}\)%
(E) 66 \(\frac{2}{3}\)%

(A) 50%
(B) 58  \frac{1}{3} %
(C) 60%
(D) 62  \frac{1}{2} %
(E) 66  \frac{2}{3} %

Edskore · Answer

Answer: (A) 50%

This is a Percent and Interest problem that catches a lot of people — the trap is jumping to the weighted average or trying to set up some formula before just assigning a clean variable.

Let P = the price Vicente actually paid for each shirt (they're the same, so both cost P).

1. Shirt 1 was marked down 75%, meaning he paid 25% of its regular price.
 So P = 0.25 * R1 → R1 = 4P.

2. Shirt 2 was marked down by some unknown percent x.
 So P = (1 - x) * R2.

3. "If he had bought the two T-shirts at their regular prices, he would have paid three times as much."
 He actually paid P + P = 2P total. Three times that is 6P.
 So R1 + R2 = 6P.

4. Plug in R1 = 4P:
 4P + R2 = 6P → R2 = 2P.

5. Now use R2 in the equation for Shirt 2:
 P = (1 - x) * 2P
 1/2 = 1 - x
 x = 1/2 = 50%.

The trap here is (C) 60% — people sometimes subtract 75% from some made-up total and arrive there. I fell for a version of this the first time I saw it. The key move is just calling the common sale price P and working from there — no system of equations, no guessing.

Answer: (A)

WorkDrop · Answer

Answer: (B)

Let S = the original/regular price of each of the T shirts. 
Hence, Actual cost price for 2 T-shirts = 2*S

Now, the price paid by Vicente for 2 T-shirts:
For 1st T-shirt= (1-0.75%)*S= 0.25%*S
For 2nd T-shirt, let x% be the percentage by which the other T-shirt was marked down, hence price paid for 2nd T-shirt= (1-x%)*S

Now, looking at the scenario- "If he had bought the two T-shirts at their regular prices, he would have paid three times as much"
The equation becomes-->
2*S= 3*

Solving the above equation, we get x= 58(1/3)%

Answer: (B)

BongBideshini · Answer

Let the regular price of the first T-shirt = P1 Let the regular price of the second T-shirt be P2

First T-shirt marked down 75%, so sale price = 0.25 * P1
Since both T-shirts were bought for the same price, second T-shirt sale price = 0.25 * P1

Total actually paid = 0.25P1 + 0.25P1 = 0.5*P1
Regular prices would have cost three times as much:
P1 + P2 = 3 * 0.5P1 = 1.5P1
P2 = 1.5P1 - P1 = 0.5P1

Regular price of second T-shirt = 0.5P1 
Sale price of second T-shirt = 0.25P1
Markdown % = (0.5P1 - 0.25P1) / (0.5P1) = 0.25P1 / 0.5*P1 = 1/2 = 50%
 Answer is A

AdarshSambare · Answer

Let the regular price of the first T-shirt = 100  
 Let the regular price of the second T-shirt = x

So, 100+x = the price Vicente actually paid for each shirt.

1. Shirt 1 was marked down 75%, he paid 25% of its price =   25 
  2. Shirt 2 was marked down by some unknown percent y. Need to find y  
  But Given Vicente bought two T-shirts for the same price = 25
   
 3. "If he had bought the two T-shirts at their regular prices, he would have paid three times as much."
He actually paid 100 + x total.  
 Three times (25+25) = 100 +x 
 3(50) = 100+x 
 x = 50 
 
 So, MP of second shirt = 50 
 and Selling price = 25 
 Discount (y) of 50%. 
  Option: A

kevincan · Answer

The main difficulty of this question is correctly interpreting same price!

adityacantstudy · Answer

i dont understand how 2 variable problems can be solved without plug in, does anyone know a way ? and can i get similar questions

RPstudy · Answer

I made this mistake as well. The original price of the two shirts are not the same. The price he bought them for was the same. So, the two differently priced shirts, once discounted, were of equal value.

Vicente bought two T-shirts for the same price. One had been

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