40 % of birds in a tree went to other place and half of the remaining died. On multiplying the numbe

M4maths Previous Puzzles

31 Oct 2013 birds

40 % of birds in a tree went to other place and half of the remaining died. On multiplying the number of remaining birds to 30, It became a perfect square number. What will be the least possible number of birds

OPtion

1) 4
2) 16
3) 36
4) 64
5) 100
6) 144
7) 196
8) 256
9) 324
10) 400

Solution

let no of birds be x
then 60 % of the birds = 0.6x
half of this = 0.3x
so if we multiply remaining to 30 we get 30*0.3x = 9x
it will be an integer only if x is integer
so we have to select x in such a way that x, 0.6x and 0.3x would be integers
and the least possible value for this will be 100

Correct Option: 5 Best Solution (24)

Suman Saurabh   11 years AGO

Let number of birds=100
40%of birds went to other tree and 30% of birds are dead.
so remaining birds are 30%.
if we multiply it by 30=30*30=900 which is a perfect square.
so number of birds=100

Like? Yes (4) | No (1)  

Sourangsu Bandyopadhyay   11 years AGO

The question here gives the answer itself!
The solution can be derived as:
Since 40% of the birds flew away.
Then let the total number of birds be 'x'.
So,
(40/100)*x=(2/5)*x=(some whole number,say k)
Now judging by the options,100 is the least number which gives k,a whole number)!!
Hence, Answer=100. [Ans]
You, don't even require to go beyond this step..

But however let's do it for formality!
Suppose,x=100
40% of 100 is 40.
No. of remaining birds=100-40=60.
Half of them flew away,so no of remaining birds=30
Then, multiplying by 30,we get
30*30=900.[Which is indeed a perfect square!!]

Like? Yes (5) | No (3)  

SHAIK SADDAM HUSSAIN   11 years AGO

only 30% of the total birds will be left on the tree so for total of 100 birds 30% will be 30 birds so if we multiply with 30, 30*30=900 which is a perfect square.. which is not possible for any in given less than 100

Like? Yes (2) | No   

Ann Mary Jolly   11 years AGO

Ans : 5)100
30*n=x^2
lowest no. x = 30, 30*n = 30^2
=> n = 30
remaining birds on tree after half died = 30
Therefore, initially there must have been 60 birds.
Since 40% birds flew away from total,60% remained.
60%(total) = 60 => total no. of birds = 100

Like? Yes (2) | No   

Divya Srivastava   11 years AGO

let the number be 'x'
0.6x did not fly away.
0.3x * 30 = 9x
for the 9x should be perfect square the least possible value of x should be 4.
But it is given that 40% of them fly away, now 40% of 4 = 1.6 which is not possible,
therefore it should be divisible by 10 or 100.
hence correct option is 5). 100.

Like? Yes (2) | No   

VIKASH KUMAR SHARMA   11 years AGO

let the no. of birds are 100.
then 40% of birds went to other place and in the remaining 60% birds. thn 50% of the remaing were died , thrfor 30*30= 900 , which is a perfect square.
thrfor the total no. of birds = 100 (ans)

Like? Yes (1) | No   

Sujeet Kumar   11 years AGO

30% of the birds remain on tree
and 30% multiplied by 30 is perfect square
which is 30= 2*3*5
so at least 2*3*5 should be there to make it perfect sqaure.
so ans is 100,so that (30/100)*100*30= prefect square.

Like? Yes (1) | No   

anil   11 years AGO

40*X/100;
REMAIN*30=900
SO REMAIN=30;
60+40=100;

Like? Yes (1) | No   

vikash kumar   11 years AGO

100*.6=60
60/2=30
or
100*.3=30birds
30*30=900perfect sq

Like? Yes (2) | No (1)  

Md Shahnawaz Shahab   11 years AGO

let the number of birds be x
therefore .4x birds fly away, and .6x birds remain. Now half of .6x birds die. Now total remaining birds = .3x
Now according to the problem 0.3x * 30 = a perfect square...
subtituting x = 100 we get 0.3x = 30 which makes it a perfet square....we didnt consider the other options as e cannot use a fraction of any bird.... 0.5 or 0.3 bird can NOT remain.

Like? Yes (2) | No (1)  

swastik   11 years AGO

ans is 100
let there is 100 birds.40 birds went to other tree. so there is only 60 bird left. out of that half died.so 30 bird left.
means only 30% bird left
now go with the option
0.4*0.3=1.2 cant be birds number
16*0.3=4.8 cant be birds number
36*0.3=10.8 cant be birds number
64*0.3=19.2 cant be birds number
100*0.3=30 it can be birds number

now check the 2nd condition
30*30=900
it is a perfect square
so 100 is the least possible ans

Like? Yes (1) | No   

prakash kumar   11 years AGO

since 40% of birds went to other place so no of birds must be a multiple of 5
there are only two options of multiple of 5
if we check for 100
if 40% went then remaining birds are 60
since half of remaining died
now remaining birds are 30
after multiplying with 30 it will be a perfect square
100 is satisfying all conditions ang is least no
den no of birds=100

Like? Yes (1) | No   

Chandni Maurya   11 years AGO

ans=100
remaining %=100-40-60/2=30
30x*30=perfect square=> min=>x=1
=>900
=>remaining min birds=30
=>total birds=30*2+40=100

Like? Yes (1) | No   

Yapadinne Raju   11 years AGO

let total birds=x,
40% of birds went means= 40x/100=2x/5
remaining birds=3x/5
in which half of the remaining birds died..=3x/(5*2)=3x/10
on multiplying the number of remaining birds to 30.....>3x/10=30
x=100

Like? Yes (1) | No   

Ranjit Somisetty   11 years AGO

.3*x*30=9x is perfect square when x is 100

Like? Yes (1) | No   

ravi singh   11 years AGO

answer is 100

40% of 100=40
remaining is =60
and 50% of 60=30

remaining is 30

30*30=300
hence option 5

Like? Yes (1) | No   

Raviranjan Pandey   11 years AGO

bcoz if u multiply with 30*30=900 ITS PERFECT SQUARE
LET 100BIRDS

Like? Yes (1) | No   

Grishma Shah   11 years AGO

given is the remaining no. of birds multiplying gives a perfect square.
Hence,
30*30=900 is a perfect square.
30 birds are remaining
Half died, results 30*2= 60
40 % flied = 60+40=100
hence 100 is the least possible birds

Like? Yes (2) | No (1)  

samiul islam   11 years AGO

We can get 40% bird by selecting two options 100 or 400..but doing other calculations it is clear that 100 will give us right ans

Like? Yes (1) | No   

moumita majee   11 years AGO

given that 40 % brds left the treee.. and remaining 30% are died..
remaining are 30%... i.e.
according to question
let X be the total num of birds
then 30% of X * 30 = perfect square
so the x will be 100
since if you find 40% of other optn then result came in fraction
but in case of 100 all condition satisfied

Like? Yes (1) | No   

HARI om kashyap   11 years AGO

given that 40 % brds left the treee.. and remaining 30% are died..
remaining are 30%... i.e.
according to question
let X be the total num of birds
then 30% of X * 30 = perfect square
so the x will be 100
since if you find 40% of other optn then result came in fraction
but in case of 100 all condition satisfied

Like? Yes (1) | No   

ishita gorai   11 years AGO

given that 40 % brds left the treee.. and remaining 30% are died..
remaining are 30%... i.e.
according to question
let X be the total num of birds
then 30% of X * 30 = perfect square
so the x will be 100
since if you find 40% of other optn then result came in fraction
but in case of 100 all condition satisfied

Like? Yes (1) | No   

Uddhav Ghodake   11 years AGO

becoz 40% of total birds means number shuld be integer so by taking 100 only least number comes as 40... and perfect square number is 900.

Like? Yes (1) | No   

b.s.venkatesh   11 years AGO

LET NUMBER OF BIRDS ARE 100.
40% BIRDS WENT TO ANOTHER PLACE SO REMAINING 60
HALF DIED-REMAINING 30
MULTYPLY WITH 30 WHICH IS 900 IS A PERFECT SQUARE.

Like? Yes (1) | No