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In the summer, water consumption is known to decrease overall by $25\%.$ A Water Board official states that in the summer household consumption decreases by $20\%,$ while other consumption increases by $70\%.$ Which of the following statement is correct?

- The ratio of household to other consumption is $8/17$
- The ratio of household to other consumption is $1/17$
- The ratio of household to other consumption is $17/8$
- There are errors in the official’s statement.

Migrated from GO Electronics 3 years ago by Arjun

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Best answer

Let the original water consumption be $X = Y + Z \quad \to (1),$ where $Y$ is the household consumption and $Z$ is the other consumption.

New water consumption $= 0.75X = 0.8Y + 1.7Z\quad \to (2)$

$(2) - 0.75(1) \implies 0.05Y + 0.95Z = 0$

which means either $Y$ or $Z$ must be negative which is not possible as both of them are consumption amount of water.

So, correct option is D. There are errors in the official’s statement.

New water consumption $= 0.75X = 0.8Y + 1.7Z\quad \to (2)$

$(2) - 0.75(1) \implies 0.05Y + 0.95Z = 0$

which means either $Y$ or $Z$ must be negative which is not possible as both of them are consumption amount of water.

So, correct option is D. There are errors in the official’s statement.