## Tuesday, 25 October 2011

### Arithmetic-11 (XAT-2010)

A manufacturer has 200 litres of acid solution which has 15% acid content. How many litres of acid solution with 30% acid content may be added so that acid content in the resulting mixture will be more than 20% but less than 25% ?
A. More than 100 litres but less than 300 litres
B. More than 120 litres but less than 400 litres
C. More than 100 litres but less than 400 litres
D. More than 120 litres but less than 300 litres
E. None of the above

Solution:

The following table depicts the stats before and after adding 30% acid solution:

 Total Qty %acid content acid content Initial Qty 200 15 200*15/100 = 30 Added Qty x 30 0.3*x Resulting Mixture 200+x 30+0.3x

“Acid content in the resulting mixture will be more than 20% but less than 25%

Proportion of Acid content in the resulting mixture = (30+0.3x)/(200+x)
20/100 < (30+0.3x)/(200+x) < 25/100
=> 1/5 < (30+0.3x)/(200+x) < ¼
We split this inequality into two parts.

1/5 < (30+0.3x)/(200+x) => 200+x < 150+1.5x
=> 50 < 0.5x => x>100  ---(1)

(30+0.3x)/(200+x) < ¼ => 120+1.2x < 200+x
=> 0.2x < 80 => x < 80/0.2 => x < 400  ---(2)
From (1) and (2), 100 < x < 400