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01 Jan 2026, 22:00
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A
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Difficulty:
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Question Stats:
84% (01:32) correct
16%
(01:09)
wrong
based on 64
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A processed coffee manufacturer sources coffee beans from precisely 3 farms. If the available stock decreased by 20% from the first farm and 30% from the second farm, by what percentage must the manufacturer increase the amount of beans sourced from the third farm to offset a decrease in available stock from the first two farms?
(1) Before the recent decrease, the total amount of beans sourced from the first, second, and the third farm was in the ratio 1:1:2.
(2) Before the recent decrease, the manufacturer sourced 50 kilograms of coffee beans from the first farm.
(1) Before the recent decrease, the total amount of beans sourced from the first, second, and the third farm was in the ratio 1:1:2.
(2) Before the recent decrease, the manufacturer sourced 50 kilograms of coffee beans from the first farm.
04 Jan 2026, 20:15
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Explanation:
Let the initial amount of beans sourced from the first, second, and third farms be A, B, and C, respectively.
Let the percentage increase in the amount of beans sourced from the third farm be r%.
The new amount of beans sourced from the third farm = C(1 + r%).
Since the available stock decreased by 20% from the first farm, the new amount of beans sourced from the first farm = 0.8A
Since the available stock decreased by 30% from the second farm, the new amount of beans sourced from the second farm = 0.7B
Since the total amount of beans sourced must be the same: A + B + C = 0.8A + 0.7B + C(1 + r%) (Equation I)
We need to find whether the value of r can be determined.
Statement (1)
A : B : C = 1 : 1 : 2
If we take the constant of proportionality as k, then A = k, B = k, and C = 2k.
Substituting these values in Equation I:
A + B + C = 0.8A + 0.7B + C(1 + r%)
k + k + 2k = 0.8k + 0.7k + 2k(1 + r%)
Canceling k from both sides,
1 + 1 + 2 = 0.8 + 0.7 + 2(1 + r%)
Since we have 1 equation with 1 unknown variable it is possible to determine the value of r. Hence, Statement (1) is sufficient.
Statement (2)
A = 50
Substituting the value of A in Equation I does not help determine the value of r. Hence, Statement (2) is insufficient.
A is the correct answer choice.
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