M4maths Previous Puzzles

20 Sep 2012 integers

The ratio of two integers is equal to the ratio of a number 9 more than the numerator (of ratio of two integers) and a number 4 times the denominator (of ratio of two integers). That ratio will be

OPtion

1) 1/8
2) 1/10
3) 4/9
4) 4/15
5) 2/17
6) 4/19
7) 5/12
8) no solution
9) infinite solutions
10) none of these

Solution

according to the given condition
x/y = (x+9)/4y
on solving x = 3 and y can take any value

Correct Option: 9 Best Solution (13)

venu chowdary   12 years AGO

let numerator be x
letdenominator be y
then x/y = (x+9)/(4y) ==> x=3 , but y can be any no
so infinite solutions are possible

Like? Yes (7) | No (3)  

sainath   12 years AGO

let x and y be the 2 integers
then x/y=(x+9)/4y
=>4x=x+9
=>x=3
but y can have any integer value...
so the x/y value has infinite solutions...

Like? Yes (8) | No (5)  

SDeep Bhattacharya   12 years AGO

(x/y)=(x+9)/4y....eqn(1)
=>4xy=xy+9y
=>3xy=9y
=>x=3
now putting x=3 in eqn(1)
we get,(3/y)=(3+9)/(4y)
=>(3/y)=12/(4y)
=>3/y=3/y...i.e,it becomes an identity.
So,for any integral value of y not equal to 0,the above will be satisfied.
So,there are infinitely many solutions for the above problem..

Hence OPTION 9) infinite solutions, is correct..

Thanks To All..:-) :-)

Like? Yes (6) | No (3)  

rachana dhekane   12 years AGO

Let the ratio=x:y
according to given conditions,
x:y=x+9:4y
Hence, x=3
For ratio to be equal
y can have any value.
Hence it has infinite solutions.

Like? Yes (5) | No (2)  

Dr.Dipin Singh   12 years AGO

If two integers are x and y , then
as per given condition
x/y = (x+9)/4y
x= (x+9)/4
4x=x+9
x=3

Hence any ratio with numerator 3 will satisfy given condition.

Like? Yes (4) | No (2)  

Ganga Prasad Bhusal   12 years AGO

suppose ratio is x/y
then x/y = (x+9)/4y
on solving it, x=3 and y = any integer
so there will be infinite soln.

Like? Yes (3) | No (1)  

Asloob Sabir   12 years AGO

3/y=12/4y



The second unknown can have any number of values, still we get the required solution,

Like? Yes (3) | No (1)  

Nitish Kumar   12 years AGO

let the ratio will be x/y.
then,
x/y=(x+9)/4Y
=>x=3 when,y!=0
y can take any integer value
so, answer will be infinite solutions

Like? Yes (3) | No (1)  

Narender Bhardwaj   12 years AGO

Let the ratio of two integer=x/y,
according to the question
x/y=9+x/4y......(1)
=>4x=9+x
=>x=3,
Hence by putting x value in (1) we get
3/y=12/4y,
Which is true for any value of y
Hence there are infinite many solutions

Like? Yes (4) | No (2)  

sridhar reddy   12 years AGO

according to the question
let the two integers x & y
x/y=(9+x)/4y
x=3 and y belongs to integer
so the ratio will be infinite solutions

Like? Yes (3) | No (1)  

vivek kumar   12 years AGO

let two integer be x and y
then ratio=x/y
now, x/y=(x+9)/4y
solving this equation we get x=3
then ratio=3/y
and y can be any integer
hence,infinite solution

Like? Yes (2) | No (1)  

Ashutosh Ranjan   12 years AGO

x/y=(x+9)/4*y where y!=0 and y!=n*x[n=1,2,...]
4*x=x+9
x=3
y can be any non-zero integer not multiple of 3.
hence 3/y gives infinite solutions...
thank you!

Like? Yes (2) | No (1)  

VIJAY CHOUDHARY   12 years AGO

let the two integer value are a and b.
now according to the question
a/b=(a+9)/4b
3a=9;
a=3;
for any integer value of b the ratio will be
3/b

Like? Yes (2) | No (2)