Latest Elitmus Aptitude Question SOLUTION: how many pairs of positive integers m,n satisfy 1/m + 4/n = 1/12, given n is odd integer less than 60 op: 3,4,5,6,7

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(#M40151540) ELITMUS Numerical Ability question Keep an EYE

how many pairs of positive integers m,n satisfy
1/m + 4/n = 1/12, given n is odd integer less than 60

op: 3,4,5,6,7

Asked In Elitmus siddharth prakash singh (9 years ago)

Unsolved Read Solution (6)

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Srayashi Das  (9 years ago)

1/m + 4/n =1/12
(n+4m)/mn =1/12
12n+48m=mn
12n=m(n-48)
m=12n/(n-48)
so, n= 49,51,53,55,57,59 and value of m should be an integer
so by putting the values of n like 49,51,57........value of m will come integer so the answer is 3

Is this solution Helpfull? Yes (57) | No (2)  

siddharth prakash singh  (9 years ago)

Actually this que was asked by one of the member but it was incomplete.

solution is:-
on solving above eq we get
12n + 48m =mn
mn - 12n - 48m = 0
adding 576 both sides, we get
mn - 12n - 48m + 576 =576
(m-12)(n-48)=576
since 576= 2^6*3^2
now if n-48 is even then
n=even+48 =even
but we req to have n as odd
so n-48 = odd
now
(n-48) * (m-12)= 2^6*3^2
(n-48) * (m-12)= 1*(2^6*3^2),,,, [n-48=1] so [n=49]
(n-48) * (m-12)= 3*(2^6*3),,,, [n-48=3] so [n=51]
(n-48) * (m-12)= 9*(2^6*3^2),,,, [n-48=9] so [n=57]
so there are 3 pairs of positive integers that satisfy the given eq with given conditions.

Is this solution Helpfull? Yes (12) | No (4)  

Pralay Bagchi  (9 years ago)

1/m+4/n=1/12
m=12(n/n-48);
hence n to be an odd integer there are 3 values to satisfy m is an integer
n=49,51,57
Apart from these values other odd ones are fraction.
so possible pairs number is 3.

Is this solution Helpfull? Yes (2) | No   

Ashima Sabharwal  (9 years ago)

1/m+1/n=1/12
or
12n+48=mn
or
mn-12n-48m-576=576
n(m-12)-48(m-12)=576
(n-48)(m-12)=576
if n is odd integer then n-48 will also be odd or rather an odd factor 576
odd facors of 576 are 1,3,9
so
n-48=1 .... n=49(n

Is this solution Helpfull? Yes | No (1)  

Arijeet Ghosh  (8 years ago)

1/m=1/12-4/n,Since m is positive, n must be greater than 48. Possible odd values of n such that 48 < n < 60 are 49, 51, 53, 55, 57 and 59 of which only 49, 51 and 57 give integral values of m.
For n=49,m= 588, n= 51,m=204 and n = 57, m=76. Ans-> Three pairs of +ve integers.

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Shivam  (7 years ago)

Why is it taken odd integers..................... since the values satisfied between the range of 48

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