Puzzles Contest - 13 With Answers

[HELP]

1. At the Fair At the fair I bought 6 pineapples and two jackfruits . for Rs. 15. If I could have bought 4 more pineapples for Rs. 14 tharijackfruitsfor.Rs. 9. What would be the I price of each?

2 . I have five sections of a necklace-each section consisting of four links. I took the sections to a goldsmith and asked him to give me an estimate to join the 5 sections. into a one piece necklace. The goldsmith wanted"Re.1 to cut open a link and Re. 1 to solder it together again. What is the cheapest method and how much should it cost me to get the five pieces joined together into one full necklace?

3. ThiS is an ancient problem dating back to about 310 A.D. Demochares had lived one-fourth of his life as a boy, one-fifth as a youth. one-third as a man. and has spent thirteen years in his dotage. Howald is Demo- chares?

4. The combined ages of Reena and Seena are 44 years and Reena is twice as old as Seena was when Reena was half as old as Seena will be when Seena is three times as old as Reena was when Reena was three times as.. old as Seena. Howald is Reena?



5. A group of us were playing Bingo. I noticed something very interesting. There were different Bingo cards with no two cards having the same set of numbers in corresponding column or row. The centre of course was a free space.How many such cards are possible, can you tell?

Answers



1. Pineapples cost Rs. 1.75 a piece and jackfruits Rs. 2.25.

2. There is only one cheapest method and that is to open the 4 links of one section and then use these links to join the other 4 sections together, whi~h should cost altogether Rs. 8.

3. Demochares must be sixty years of age.

4. The ratio of Reena' s age to Seena's must be as 5 to 3. Since the sum of their age is 44, Reena must be 271/2 and Seena 16112.


5. The N column is the most restrictive column since it has only four open choices, instead of the five usual choices. These four choices must be made from the set (31, 32, 33,43, 44, 45) which contain fifteen elements. Thus when we have made all possible selections of 4 numbers from 15 numbers, we will have reached the total possible number of different Bingo cards.
( 15 = 15* 14*13* 12 = 1365
4 4 * 3 * 2 * 1
Edited by: HELP

[Hemanth_2u]

1. At the Fair At the fair I bought 6 pineapples and two jackfruits . for Rs. 15. If I could have bought 4 more pineapples for Rs. 14 tharijackfruitsfor.Rs. 9. What would be the I price of each?


Small Request to Swoumya garu and Keerthi Garu. Please give Answers with solutions.


Solution:
Let p be the price of one pineapple nd let j be the price of one kacjfruit,

As per question,
6p+2j=15 -----(1)
Also let the there be y number of jackfruits purchased at Rs. 9
then, y * j =9 --- (2)
Also as per question,
(y+4)*p =14 ----(3)
solving eqns 1,2 & 3 :
p=1.75
j=2.25

[Hemanth_2u]

3[/b]. ThiS is an ancient problem dating back to about 310 A.D. Demochares had lived one-fourth of his life as a boy, one-fifth as a youth. one-third as a man, and has spent thirteen years in his dotage- How old is Demo-chares?
Ans: Let Demochares lived in x years
As a boy had lived = x/4
As a youth had lived = x/5
As a man had lived = x/3
spent thirteen years in his dotage
x/4+x/5+x/3+13 = x
x = 130 Years

[Hemanth_2u]

4. The combined ages of Reena and Seena are 44 years and Reena is twice as old as Seena was when Reena was half as old as Seena will be when Seena is three times as old as Reena was when Reena was three times as.. old as Seena. Howald is Reena?


Solution:


Let the present age of reena be r and seena be s
Then r+s=44 ---(1)

Now we will go srep by step as prob goes .....

reena is twice as old as seena was

lets consider x years back from now ......

then , r=2(s-x) ---(2)

when reena was half as old as seena will be

lets consider y years ahead from now

then , r-x = (s+y)/2 ........(3)

when seena is 3 times as old as reena was

lets consider z years back from now ......

(s+y) = 3(r-z) ...........(4)

when reena was 3 times as old as seena

(r-z)=3(s-z) .................(5)

Solving all these eqns we get ,
s=16.5
r=27.5

[keerthi]

Hi hemanth,


Well i hope for what ever questions i have answered till now i gave solutions for each and every question.I dont know why u mentioned it like that.If there is anything wrong post ur explanations.

[keerthi]

2 I have five sections of a necklace-each section consisting of four links. I took the sections to a goldsmith and asked him to give me an estimate to join the 5 sections. into a one piece necklace. The goldsmith wanted"Re.1 to cut open a link and Re. 1 to solder it together again. What is the cheapest method and how much should it cost me to get the five pieces joined together into one full necklace?

Ans) 8 Rs
Sol: In order to join 5 sections we need to cut 4 links of four sections and agian join 4 links to make it a one piece necklace.
hence cheapest way to do this is with 4+4 = 8Rs