Let the different number be P and Q.
Let the divisor be represented by A.
let us take some real life assumption in solving solving this question. The assumptions would be stated as we progress.
Recall from the question:
1) P/A gives reminder 11
2) Q/A gives remainder 21
3) (P+Q)/A gives remainder 4
Let digress a bit by considering this short example below:
say P=15 & A=2
15/2= 7 r 1 (r=remainder)
finding an expression for 15 in terms of the quotient (7), remainder(1) and the divisor (2).
Now going back to the question,
P/A= 1 r 11
NB: we assume that A can only go in P once.
P=11+ (A*1)
P=A+11 ------------(i)
similarly with the same assumption,
Q/A=1r21
Q=21+(A*1)
Q=A+21------------(ii)
from i and ii, we can get equation representing the value of A.
A=P-11 ---------iii
A=Q-21 ----------iv
since A=A, the P-11=Q-21 -------------v
Note that from the question, it was given that (P+Q)/A gives r=4
so, from eqn (v), P-Q = 11-21
P=Q=11+21 (assumption stated)
P+Q=32
32/A= 1 r4
assuming that A can be found once in 32.
from the example that 32=4+(1*A)
32=4+A
A=28
Thus, the divisor is 28. option B is the correct option
