Question

when a number is devided by 13 the remainder is 11 and when the number is devided by 17 the answer reminder is 9 find the number?

Answer 1

Let x be the number,
Case (i):-
x=13p+11
Case (ii);-
x=17q+9

Where p,q are quotients for case (i) and (ii) respectively,

13p+11=17q+9
13p+11-9=13q+4p
13p=13q+(4q-2)
Divide 13 on both sides,
13p/13=q+(4q-2)/13
p=q+(4q-2)/13

Put different values of q where (4q-2) is divisible by 13,
Put q=7,
p=7+[4(7)-2]/13
p=7+(28-2)/13
p=7+(26/13)
p=7+2
p=9

put p=9 in x=13p+11
x=13(9)+11
x=117+11
x=128

If 128 is there in the option, it is the answer otherwise,
put q=7+13=20,
p=20+(4(20)-2)/13
p=20+(80-2)/13
p=20+78/13
p=20+6
p=26

Put p=26 in x=13p+11
x=13(26)+11
x=338+11
x=349

So,answers are 128 or 349.

Hope it helps