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03 Aug 2024, 23:45
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
44% (02:59) correct
56%
(03:07)
wrong
based on 80
sessions
History
Date
Time
Result
Not Attempted Yet
On buying 3 t-shirts, the shopkeeper gives a total discount of $120. When buying 4 t-shirts, he gives 1 t-shirt for free. It is known that the shopkeeper earns a 20% profit in both cases. What is the marked price of a single t-shirt?
A. 150
B. 160
C. 170
D. 200
E. 250
A. 150
B. 160
C. 170
D. 200
E. 250
13 Aug 2024, 10:11
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I tested the options for this question.
I started with Option D, because 200 is a rather easier number to deal with.
If Marked Price (MP) is 200 then,
MP of 3 t-shirts : 200*3= 600
Total discount offered : 120
Final SP : 600-120=480
Profit on 480 is 20%, i.e. 480*20/100 = 96
Therefore, Cost Price for 3 t-shirts : 480-96=384
Price per t-shirt : 384/3 = 128
Now, MP of 4 t-shirts : 4*200 = 800
Profit on 800: 800*20/100 = 160
Therefore, cost price for 5 shirt: 800-160 = 640
Price per t-shirt : 640/5= 128
Therefore, D is the correct answer.
P.S. I tried to make this a detailed answer for better understanding, while solving, it is a rather quick method.
I started with Option D, because 200 is a rather easier number to deal with.
If Marked Price (MP) is 200 then,
MP of 3 t-shirts : 200*3= 600
Total discount offered : 120
Final SP : 600-120=480
Profit on 480 is 20%, i.e. 480*20/100 = 96
Therefore, Cost Price for 3 t-shirts : 480-96=384
Price per t-shirt : 384/3 = 128
Now, MP of 4 t-shirts : 4*200 = 800
Profit on 800: 800*20/100 = 160
Therefore, cost price for 5 shirt: 800-160 = 640
Price per t-shirt : 640/5= 128
Therefore, D is the correct answer.
P.S. I tried to make this a detailed answer for better understanding, while solving, it is a rather quick method.
14 Aug 2024, 04:40
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Discount = MP - SP (Marked Price - Selling Price)
3 T-shirts got a discount of $120 => 3*(MP - SP) = $120 => MP-SP = 40 ----(1)
4 T-shirts got a discount of 1 T-shirt => 4*(MP-SP) = 1*(SP) => 4MP = 5 SP ----(2)
Substituting (2) in (1), (5/4)*SP - SP = 40 => SP = 160; MP = (5/4)*160 = 200 [D is the answer]
3 T-shirts got a discount of $120 => 3*(MP - SP) = $120 => MP-SP = 40 ----(1)
4 T-shirts got a discount of 1 T-shirt => 4*(MP-SP) = 1*(SP) => 4MP = 5 SP ----(2)
Substituting (2) in (1), (5/4)*SP - SP = 40 => SP = 160; MP = (5/4)*160 = 200 [D is the answer]
