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02 Feb 2023, 10:45
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
61% (02:50) correct
39%
(03:03)
wrong
based on 105
sessions
History
Date
Time
Result
Not Attempted Yet
A shopkeeper buys two printers A and B. Had the shopkeeper paid the full price of both printers, they would have cost the same to him. However, he buys printer A with a down payment of 10 percent of the cost of printer A and printer B with a down payment of 20 percent of the cost of printer B and repays the remaining cost and the individual finance charges of the printers A and B over a period of time. The finance charges for printers A and B are equal to 40 percent of the remainder of the cost of printer A and y percent of the remainder of the cost of Printer B respectively. What should be the value of y so that the cost of buying the two printers is equal for the shopkeeper?
A. 40%
B. 45%
C. 50%
D. 55%
E. Cannot be determined
A. 40%
B. 45%
C. 50%
D. 55%
E. Cannot be determined
kaustubh1305
Joined: 05 Jan 2023
Last visit: 22 May 2025
Posts: 10
Given Kudos: 10
Location: India
Schools: LBS '26 (D) Ross '26 (D) Sloan '26 (D) Judge '25 (D) Tuck '26 (D) Tepper '26 (WL) Kenan-Flagler '26 (A)
GMAT 1: 730 Q50 V38
GPA: 4
Schools: LBS '26 (D) Ross '26 (D) Sloan '26 (D) Judge '25 (D) Tuck '26 (D) Tepper '26 (WL) Kenan-Flagler '26 (A)
GMAT 1: 730 Q50 V38
Posts: 10
06 Mar 2023, 10:11
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Let the cost of printer A be x.
Now, cost of printer B will also be x (as it is mentioned " Had the shopkeeper paid the full price of both printers, they would have cost the same to him")
After paying 10% in down payment for printer A, remaining amount = 0.9x
Similarly, after paying 20% in down payment for printer B, remaining amount = 0.8x
Now, finance charges for printer A = 40% of remaining amount = 0.4*0.9x = 0.36x
For the shopkeeper to have equal cost of buying, finance charges should be same for printer B too.
Therefore finance charges for printer B = 0.36x
But, finance charges for printer B = y% of remaining amount = 0.y*0.8x
Equating both the equations and solving for y, we get
y=0.45 = 45%
Cheers
Now, cost of printer B will also be x (as it is mentioned " Had the shopkeeper paid the full price of both printers, they would have cost the same to him")
After paying 10% in down payment for printer A, remaining amount = 0.9x
Similarly, after paying 20% in down payment for printer B, remaining amount = 0.8x
Now, finance charges for printer A = 40% of remaining amount = 0.4*0.9x = 0.36x
For the shopkeeper to have equal cost of buying, finance charges should be same for printer B too.
Therefore finance charges for printer B = 0.36x
But, finance charges for printer B = y% of remaining amount = 0.y*0.8x
Equating both the equations and solving for y, we get
y=0.45 = 45%
Cheers
15 Apr 2024, 08:39
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Hi Bunuel and kaustubh1305 - I keep getting 32.5% as the answer for this question, and I'm not sure why. I've also checked with an online calculator, and 32.5% seems to work, per my setup. Is something wrong with my setup?
Setup:
Call the cost of Printers A and B c dollars each. We have:
0.1c+(0.4)(0.9c)=0.2c+(y/100)(0.8c)
Cancelling out the variable c since it is common to both sides and non-zero and simplifying, we have:
0.1+0.36-0.2=(y/100)(0.8)
Solving, we get y=[(0.26)(100)]/(0.8)=65/2=32.5%.
Where did I go wrong here? I have solved it now multiple times and can't seem to find my mistake.
Setup:
Call the cost of Printers A and B c dollars each. We have:
0.1c+(0.4)(0.9c)=0.2c+(y/100)(0.8c)
Cancelling out the variable c since it is common to both sides and non-zero and simplifying, we have:
0.1+0.36-0.2=(y/100)(0.8)
Solving, we get y=[(0.26)(100)]/(0.8)=65/2=32.5%.
Where did I go wrong here? I have solved it now multiple times and can't seem to find my mistake.
