Question

(p+q) is two digit number 29, if q is in the units place then p=
1)6
2)9
3)5
4)3​

Answer 1

PQ and QP can be written in following ways

PQ = 10P+Q (Example: 21=10(2)+1)

QP = 10Q+P

PQ+QP = 10P+Q+10Q+P = 11(P+Q)

Given that PQ+QP = RSR

so, RSR = 11(P+Q)

-> RSR is a multiple of 11

Since it is given that the unit's digit and the hundred's digit are same i.e R

The need to be multiplied by either 11 (11*11 = 121), 22(11*22 = 242), 33....

But P+Q cannot exceed 18(as the max possible single digit integer is 9)

So, P+Q = 11 and RSR = 121