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Given
1/p + 4/q = 1/12  
 q is odd and 0< q <60

first find the value of p in terms of q .

1/p = 1/12 - 4/q
1/p = (q - 48 )/ 12q
p = 12q / (q - 48 ) .....(i)

that means q is always greater than 48 , i.e q>48 thats because (q-48) is positive number

so we can say 48<q<60 ...(ii) and q is odd given .
and to satisfy (i) these odd values of q are 49,51,53,55,57,59 .

Now put each value of q in equation (i)
p = 12 * 49 / ( 49 - 48) = 588 / 1= 588
p= 12 * 51 /(51-48) = 612/3 = 204
p= 12 * 53/(53-48) = 636/5 = 127.2 [ not an integer, it's a fraction ]
p = 12 * 55/(55 - 48) = 660/7= 94.28 [ again not an integer ]
p = 12 * 57/(57-48) = 684 /9 = 76
p= 12 *59 /(59-48) = 708/11= 64.36 [ not an integer ]

so possible q value that satisfy given conditions are 49,51,57 .
that pair (p,q) that satisfy given conditions are (588,49) (204,51) (76,57) .

so number of pairs are 3 .
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3 pairs are possible for q = 49, 51 and 57
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