simplification aptitude questions
12.  Free notebooks were distributed equally among children of a class. The number of notebooks each child got was oneeighth of the number of children. Had the number of children been half, each child would have got 16 notebooks. Total how many notebooks were distributed ?  
Answer: Option C Explanation:
Let total number of children be x.

13.  A man has some hens and cows. If the number of heads be 48 and the number of feet equals 140, then the number of hens will be:  
Answer: Option D Explanation:
Let the number of hens be x and the number of cows be y. Then, x + y = 48 …. (i) and 2x + 4y = 140 x + 2y = 70 …. (ii) Solving (i) and (ii) we get: x = 26, y = 22. The required answer = 26. 
14. 


Answer: Option B Explanation:
= 4 (where a = 469, b = 174.) 
15.  David gets on the elevator at the 11^{th} floor of a building and rides up at the rate of 57 floors per minute. At the same time, Albert gets on an elevator at the 51st floor of the same building and rides down at the rate of 63 floors per minute. If they continue travelling at these rates, then at which floor will their paths cross ?  
Answer: Option C Explanation:
Suppose their paths cross after x minutes. Then, 11 + 57x = 51 – 63x 120x = 40
So, their paths cross at (11 +19) i.e., 30^{th} floor. 