GATE2017 EC-1: GA-3

Question

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?

• A. The ratio of household to other consumption is $8/17$
• B. The ratio of household to other consumption is $1/17$
• C. The ratio of household to other consumption is $17/8$
• D. There are errors in the official’s statement.

Comments

https://gateoverflow.in/139101/gate-2017-ece-set-1

Answer 1

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.

Comments

From where did you derive 0.95 @Arjun Sir, I tried many times but not able to understand. Please help

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@ ankit3009, multiplying equation  $1$ by   $0.75$  and then subtracting it from equation  $2$ gives  $0.05Y+0.95Z=0$   i.e.   $1.7-0.75=0.95$