well bmin is not 10

It is actually ....................... Youwant me to tell u ???

ne way   Kirpal

could u please explain in detail how u r telling bmin is 10 . In that process u may find ur error

My attempt:

a+11b = 13  

a+13b = 11

Eliminating b we get 2a = 169  - 121  

Also 2b = 11 - 13

Hence 2(a+b) = 156 - 110

1 and 2, and  11 - 13   0 and  and  are of the same parity and hence the least difference is 2

give up!

 no value of a+B exists as such.....

2a = 169  - 121  .....................................1

2b = 11 - 13 ..................................................2

a+b = 78 - 55 .................................................3

since a and b are natural no.s(as mentioned by author of this ques)...from eqn 1

    169  121 

=>  (121/169) 

=> (1.18) .....................................4

also from eqn.2

11  13 

=>  (13/11) 

=>  (1.39) ..................................5

thus from eqn (4) and (5) no such value of a and b exists..

my try.....

a + 11b=13m

a + 13b=11n

solving we have a= (169m-121n)/2

and b=(11n-13m)/2

and a+b =(156m-110n)/2...........1)

now as a>0 and b>0

we have.....   11/13> m/n>121/169

or 0.85 > m/n > 0.72

we take a favourable case of 0.75to get m and n as close to each other as possible so as to get the minimum value of the expression of 1)

due to which m/n=3/4.....m=3c and n=4c.......for integral values of a+b , c shud be even and 2 being the min evn number we have m=6 and n=8

using this we have min(a+b) as (936-880)/2 = 56/2 = 28....

so the minimum value of the expression (a+b) = 28.....

justification for using 0.75 as m/n ratio....

to produce min value of a+b......(153m-110n)/2 shud be minimum rite....nd 0.72<m/n<0.85......tell me the 2 evn integers such that they are in the ratio that differs frm 0.72 by the minimum and also the difference btween the two is minimum....=2 the minimum difference between 2 evn numbers(unequal)....u will say numbers like 6 and 8......(ratio 0.75) 10 and 8( ratio 0.8 but not closer to 0.72 than 0.75) u may say 10 and 12.....( ratio =0.833 but not as close to 0.72 as 0.75) in the same way u cud take a number of couples.....but u will find that the minimum difference btween 0.72 and the m/n ratio will only be achieved in the case of 6 and 8....if u go one step down taking 6 and 4...ull land up in truble as ratio is 0.66 which is out of the eqn...

so clearly the two integers m and n are 6 and 8 inserting which we get the min value of (a+b) as 28...

tell me whether its rite or wrong.....