# Day-3 | Aptitude Questions and Answers with Explanation

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1. John is supposed to walk from his house to park every morning. One morning he is in real hurry and wants to save atleast 1/3rd of the time. By how much percentage he should increase his speed.

a)      100%   b)  33%   c)  66%        d)  50%

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Let the distance between his house and park be 100 metres.

Let’s assume he takes 30 minutes daily. Hence his speed would be 100/30.

One day, if he wishes to save 1/3rd of 30 minutes, that is 10 minutes, he should cover the distance in 20 minutes in which case his speed would be 100/20.

Required increment in speed = (Required increment in speed / Original Speed) * 100 % = ((100/20 – 100/30)/100/30)* 100% = 50%

2. Can you give a simple formula to find average of sum of squares of first n natural numbers?

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Answer: (n + 1) (2n + 1) /6 can be used to calculate the average of sum of first n natural numbers.

3. Given Log x (ab) and logx (a/b), how you will find logx a

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Answer:  Log x (ab) can be written as logx (a) + logx (b) ……..equation 1.

logx (a/b) can be written as logx (a)  – logx (b) ……..equation 2.

Solving equation 1 and 2 we will get  logx (a) =  Log x (ab) + logx (a/b)/ 2)

4 .Consider a rhombus with diagonals of lengths d1 and d2. What could be its area?

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Answer: Area of the rhombus = ½(d1 * d2)

5.Can you quickly tell the ratio of the volume of a cylinder of height h to that of another cylinder of unit height but with same radius?

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