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Mathematical Reasoning

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Now many competitive examinations have started asking questions under mathematical reasoning. The questions that are asked under this chapter are based on mathematical rules, whose purpose is to assess the general intellectual capacity of the candidates.

**Derived Example**

**Example 1.** How many least number fishes can float by making the given formation, two fish in front of a fish, and two fish behind a fish and one fish between two fishes ?

** (a)** five** **** (b)** seven** **** (c) **four** **** (d) **three

** Solution: **(d)

Therefore, at least three fishes can float by this formation.

** Example 2. **How long a monkey will take to touch the top of a tree of 60 feet tall, if it climb 3 feet in one second and instantly falls 2 feet?

** (a) **60 seconds** **** (b) **50 seconds** **** (c) **58 seconds** **** (d) **57 seconds

** Solution: **(c) Total length of tree = 60 feet, monkey climb 3 feet in one second and falls 2 feet i.e. in 1 second it only climbs up 1 (3-2) feet.

Monkey climbs up to 1 feet = 1 second

It will climb 57 feet = 57 seconds and the remaining 3 feet will climb in the next second.

Hence the total time taken to climb the tree by the monkey = 57 + 1 = 58 seconds

** Example 3. **Some oranges were equally divided among 40 children . If 20 more children will be there then each child will get 5 less Oranges. How much Oranges was distributed in the beginning?

** (a) **200** **** (b) **300** **** (c)** 400** **** (d) **600

** Solution: **(d) Initially the number of Oranges that each child receives = X

Then the total number of Oranges in the beginning = 40 × x = 40x

After increasing 20 children the number of Oranges that each child receives = X – 5

Therefore (40 + 20) = the number of oranges received by 60 children = 60 (X – 5)

Now, according to the question,

60 (x-5) = 40x

⇒ 60x – 300 = 40x

⇒ 20x = 300

⇒ x = 15

So the number of Oranges distributed in the beginning = 40x = 40 × 15 = 600

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