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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?

1. The ratio of household to other consumption is $8/17$
2. The ratio of household to other consumption is $1/17$
3. The ratio of household to other consumption is $17/8$
4. There are errors in the official’s statement.
Migrated from GO Electronics 3 years ago by Arjun

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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.
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From where did you derive 0.95 @Arjun Sir, I tried many times but not able to understand. Please help
@ ankit3009, multiplying equation  $1$ by   $0.75$  and then subtracting it from equation  $2$ gives  $0.05Y+0.95Z=0$   i.e.   $1.7-0.75=0.95$

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