Out of a group of ducks, 7/2 times the square root of the number are swimming in water while two rem

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13 May 2016 Number of ducks

Out of a group of ducks, 7/2 times the square root of the number are swimming in water while two remaining are playing on the shore. The total number of ducks is

OPtion

1) 2
2) 4
3) 6
4) 8
5) 10
6) 12
7) 14
8) 16
9) 18
10)None of these

Solution

Let the number of ducks be x.
Then, 7/2 sqrt(x) + 2 = x
=> 2x - 7 sqrt(x) - 4 = 0
=> (2y+1)(y-4) = 0
=> y = -1/2 or y = 4
=> sqrt(x) = -1/2 or sqrt(x) = 4
=> x = 1/4 or x = 16
Therefore
x=16 (Number of ducks can not be a fraction)
Option 8)

Correct Option: 8 Best Solution (6)

RAHUL KUMAR   8 years AGO

Let the total number of ducks = x^2
Now, if out of a group of ducks,
7/2 times the square root of the
number are playing on the shore, that is
no of duck swiming in water = 7/2√x^2= 7x/2
and Number of ducks playing in
shore = 2
∴According to the question,
Total number of ducks =
Number of duckss playing at shore + Number of ducks playing in water
x^2 = 7x/2 + 2
2x^2 = 7x + 2
by solving above eq, we get
x = 4 or x = -1/2
x cant be negative
so x= 4
So, the mathematical concept
used in above problem is
quadratic equation.
Thus, the total number of
duck = x^2 = 4^2 = 16

Like? Yes (8) | No (2)  

ABHINAV PUSHPAM   8 years AGO

Let x = number on shore.
So the total is x + 2.
a/c question
(7/2)*root(x+2) = x.
using the quadratic formula to solve for x and we will get x=14.
So the total ducks is16.
Option 8)

Like? Yes (7) | No (4)  

Mukund Manohar   8 years AGO

Let the total number of ducks = x^2
No. of ducks swimming in water = 7/2(sq.root x^2)
=7x/2
Total number of ducks
=> x^2 = 7x/2 + 2
=> 2x^2 = 7x + 4
=> 2x^2-7x-4 = 0
=> 2x^2-8x+x-4 = 0
=> (2x + 1)(x - 4) = 0
=> x = -1/2 or x = 4
x can't be negative,so x = 4
Total no. of ducks = x^2 = 4^2 = 16

Like? Yes (4) | No (4)  

Lenin   8 years AGO

16 is the answer. because it satisfies the given condition.
so, option 8.

Like? Yes (1) | No (2)  

Pooja Priti   8 years AGO

let the number of total ducks be x.
then accrdng to quest.
x=7/2*square root of x+2
then on squaring both side we get a quadratic eq.and its roots will be:
x=(65+63)/8=16
therefore the total no.of ducks are 16.

Like? Yes | No (3)  

Bibhuti Panda   8 years AGO

(7/2)*?x + 2 = x

That's it!!! Solve it. Enjoy Maths

Like? Yes | No (5)