GATE EC 2017 Set 1 — Question 58
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Question
In the summer, water consumption is known to decrease overall by . A Water Board official states that in the summer household consumption decreases by , while other consumption increases by .Which of the following statements is correct?
Correct answer
(D) There are errors in the official's statement.
Solution
Let be the initial household consumption and be the initial other consumption. The total initial consumption is .
According to the problem, the actual summer consumption is .
The official states that summer household consumption is and other consumption is .
For the official's statement to be consistent with the overall decrease:
Since and must be positive values (representing consumption), will always be greater than zero. Thus, no positive values of and can satisfy this equation, making the official's statement mathematically impossible. Therefore, there are errors in the official's statement.
According to the problem, the actual summer consumption is .
The official states that summer household consumption is and other consumption is .
For the official's statement to be consistent with the overall decrease:
Since and must be positive values (representing consumption), will always be greater than zero. Thus, no positive values of and can satisfy this equation, making the official's statement mathematically impossible. Therefore, there are errors in the official's statement.
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