SOLUTION: In an examination,53% students passed in maths,61% passrd in physics,60% passed in chemistry,24% passed in maths and physics,35% passed in physics and chemistry,27% passed in maths

Let M be the set (and at the same time the percentage) of those who passed Math (53%)

    P ------------------------------- " --------------------------------- Physics (61%)

    C ------------------------------- " --------------------------------- Chemistry (60%)

    MP ------------------------------ " --------------------------------- Math and Physics (24%)

    PC ------------------------------ " --------------------------------- Physics and Chemistry (35%)

    MC ------------------------------ " --------------------------------- Math and Chemistry (27%)
   
    N ------------------------------- " --------------------------------- in none


This "none" I interpret in a way that these 5% are not included to either of the categories above and complement the set to 100%.


Then the only unknown is the intersection MPC of the three sets M, P and C.


It is easy to find the measure (the percentage) of MPC.


From the elementary set theory we have this equation


    100% = 5% + M + P + C - MP - PC - MC + MPC,    (*)


which gives you  


    MPC = 100 - 5 - 53 - 61 - 60 + 24 + 36 + 37 = 18%.


Now,  in the ratio you want to get, the numerator is  MC - MPC = 27% - 18% = 9%;

                                  the denominator is  PC - MPC = 35% - 18% = 17%.


Therefore, the ratio under the question is equal to  .