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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 statements 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 officials statement.

1 Answer

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Correct statement is

(D) There are errors in the officials statement.

water consumption is known to decrease overall by 25%.

Let overall water consumption is x so after decrese overall consumption is (1-0.25)x .

A water Board official states that in the summer household consumption decreases by 20% while other consumption increases by 70%. 

so let household consumption is h , after decrease by 20% it becomes (1-0.2) h 

and other consumption becomes after increase (1+0.7) (x-h) .

As overall  consumption is x and household consumption is h so other consumption is ( x-h ) .

now according to given statement , the equation becomes :

(1-0.2) h + (1+0.7) (x-h) =  (1-0.25)x

=> 0.8 h + 1.7x - 1.7h = 0.75x

=> 1.7x - 0.75x = 1.7h - 0.8h

=> 0.95 x = 0.9 h  

so h = 0.95 x / 0.9  .... (i) 

now,  looking at the options given , it tells  " The ratio of household to other consumption " ..

that means h/x-h = The ratio of household to other consumption ....(ii)

now , put h value in terms of x  in (ii) 

from (i) we get value of h and put that into (ii) , we get  {0.95 x / 0.9 }  / x - { 0.95 x / 0.9 } 

=> 1.055 x / x - 1.055x  

=> 1.055 / -(0.055)

=> - 19.1818

so The ratio of household to other consumption we get -(19.1818) .

Now check each option one by one ..

statement 1 : The ratio of household to other consumption is 8/17 = 0.470  , not match .

statement 2 : The ratio of household to other consumption is 1/17 = 0.0588 , not match 

statement 3 : The ratio of household to other consumption is 17/8 =  2.125  , not match 

so all three options are not match with our value -19.18 ..and also a ratio can not become -ve so that means there is some error in official statement !

Hence correct option is option D , There are errors in the officials statement.

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