There are 12 members between P and Q and 8 members between A and D, who is 5th to the left of Q. F, who is sitting 7th from the right end, is also 6th to the right of A. H is sitting third to the left of P, and there are 13 members to the left of P. How many members are in the row?
Solution
P _ _ _ _ _ _ _ _ _ _ _ _ Q or Q _ _ _ _ _ _ _ _ _ _ _ _ P
A _ _ _ _ _ _ _ _ D _ _ _ _ Q or D _ _ _ _ Q _ _ _ A
We are told that F is sitting 6th from the right of A and also 7th from the left end.
A _ _ _ _ _ F _ _ _ _ _ _
From this, we can infer that 13 is from the left end. So, the first arrangement of ADQ (A _ _ _ _ _ _ _ _ D _ _ _ _ Q) is not possible.
D _ _ _ _ Q _ _ _ A _ _ _ _ _ F _ _ _ _ _ _
Now, we have two cases.
i) D _ _ _ _ Q _ _ _ A _ _ _ _ _ F _ _ P _ _ _
ii) P _ _ _ _ _ _ _D _ _ _ _ Q _ _ _ A _ _ _ _ _ F _ _ _ _ _ _
We are told that H is sitting third to the left of P. In case i, F is sitting third to the left of P. So, only case 2 is possible.
We are told that there are 13 members to the left of P.
Now the total number of people is 13+30 = 43
