Math in Tenali Ramalinga’s puzzle on elephants

          I came to know about this story through my friend. This is about a problem solved by the great Tenali Ramalinga. I always enjoy Ramalinga’s stories and this is one among those tales:

An old man had three sons. During his life time he acquired 17 elephants (Exactly do not remember whether they are elephants or horses. Let us consider elephants for example). He wrote a note which specifies how these elephants shall be distributed among his three sons after his death. The note says:

“Half of the elephants shall be given to the eldest son. Two third of the remaining shall be give to the second son.  Two third of the remaining shall be give to the third son.”  

Finally the day came and the elephants needed to be distributed among the sons according to the note. But how can it be done? How can we divide 17 elephants such that the eldest son gets half of the share?

CSAT 2013 Solved Paper (paper-II)

1. In a rare coin collection, there is one gold coin for every three non-gold coins. 10 more gold coins are added to the collection and the ratio of gold coins to non-gold coins would be 1:2. Based on the information, the total number of coins in the collection now becomes

(a)90      (b)80     (c)60      (d)50

Solution:

Initial ratio = G:N = 1:3                   ---(1)

After adding 10 gold coins, the ratio becomes (10+G):N =  1:2     ---(2)

On solving (1) & (2), we get, G=20 and N=60.

Presently, the total number of coins in the collection = (10+G)+N= 10+20+60=90

Ans: (a)

2. A gardener has 1000 plants. He wants to plant them in such a way that the number of rows and the number of columns remains the same. What is the minimum number of plants that he needs more for this purpose?

(a)90      (b)24     (c)32      (d)34

Solution:

If the number of rows and number of columns are to be equal, then the total number of trees will be in the form of x², which is nothing but a perfect square. As 1000 is not a perfect square, we need to check for a perfect square above and nearest to 1000.

It’s 1024, which is square of 32. So he needs to add 24 more trees to get 1024.

Ans: (b)

Numerator/Denominator confusion

I observed that a bit of confusion prevails while simplifying fractions. The confusion is about which number will go to numerator part and which number will go to denominator part. This post is intended to clear the confusion.

Consider a fraction in the form (a/b)/(c/d).

Let us call the variables like this:

a – Numerator-numerator

b – Numerator-denominator

c – Denominator-numerator

d – Denominator-denominator

Stuff for school kids (standard 5 to 10)

I thought of providing some stuff for students studying in the range 5^th to 10^th standard. This stuff is a combination of two sets. One is Math&Logic based and the other is Knowledge based. This stuff is a mix of some questions that are based on math fundamental concepts and remaining questions that are based on commonsensical and out-of-box thinking. These do not look like standard questions that are given in school-level exams but mostly resemble or can act as base for the math and logic aptitude sort of questions that are asked in various entrance exams. My primary intention is to inculcate in kids an interest and liking on maths. I strongly opine that math solving skills are very much needed to excel in diverse fields of studies ranging from Science, Engineering to Economics, Management studies etc.

To be frank on my part, I am starting this post with small number of questions at hand but I will try to enrich this bit bank by updating it from time to time.