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07 Dec 2021, 09:18
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
66% (01:32) correct
34%
(01:40)
wrong
based on 164
sessions
History
Date
Time
Result
Not Attempted Yet
A shopkeeper made a profit of more than $16 after selling it at a profit of 20%. What could be the minimum cost price of the item, if the cost price is an integer?
A. 79
B. 80
C. 81
D. 82
E. 83
A. 79
B. 80
C. 81
D. 82
E. 83
11 Dec 2021, 08:19
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Here is the OE
Solution:
Step 1: Understand Question Statement
Profit > $16
Percentage profit = 20%.
We need to find the minimum value of CP.
Step 2: Define Methodology
We know that \( SP = CP * (1 + \frac{p}{100})\)
\(SP = CP * (1 + \frac{20}{100}) ⟹ SP = CP * (1 + \frac{1}{5}) ⟹ SP = \frac{6CP}{5}\) …(i)
We know that \(Profit > $ 16\)
Or in other words \(SP – CP > $ 16\)…(ii)
Now, we need to substitute the value of SP from equation (i) in equation (ii) and figure out the minimum value of CP.
Step 3: Calculate the final answer
SP – CP > $ 16…(ii)
⟹ \(\frac{6CP}{5} – CP > $ 16\)
⟹ \(\frac{CP}{5} > $ 16\)
⟹ \(CP > $ 80\)
Since, CP is an integer, the minimum value of CP can be $81. Hence, the correct answer is Option C.
Solution:
Step 1: Understand Question Statement
Profit > $16
Percentage profit = 20%.
We need to find the minimum value of CP.
Step 2: Define Methodology
We know that \( SP = CP * (1 + \frac{p}{100})\)
\(SP = CP * (1 + \frac{20}{100}) ⟹ SP = CP * (1 + \frac{1}{5}) ⟹ SP = \frac{6CP}{5}\) …(i)
We know that \(Profit > $ 16\)
Or in other words \(SP – CP > $ 16\)…(ii)
Now, we need to substitute the value of SP from equation (i) in equation (ii) and figure out the minimum value of CP.
Step 3: Calculate the final answer
SP – CP > $ 16…(ii)
⟹ \(\frac{6CP}{5} – CP > $ 16\)
⟹ \(\frac{CP}{5} > $ 16\)
⟹ \(CP > $ 80\)
Since, CP is an integer, the minimum value of CP can be $81. Hence, the correct answer is Option C.
