There are two buildings P and Q. If 93 persons are sent from P to Q, then number of persons in each building is same...

Question

There are two buildings P and Q. If 93 persons are sent from P to Q, then the number of persons in each building is the same. If 109 persons are sent from Q to P, then the number of persons in P is double the number of persons in Q. How many persons are there in building P and building Q?

Answer 1

699 persons are there in building P and 513 persons are there in building Q.
With the following steps we can get the answer:
Let us take persons in Building P is A, and Q is B.
Then,
A - 93 = B + 93
So, B = A - 186 ----- (1)
Similiarly,
A + 109 = ( B - 109 ) * 2
So, 2B = A + 327 ---- (2)

Subtract (1) from (2)
2B = A + 327 -
B = A - 186

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B = 0 + 513

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Then, B put in to (1)
513 = A - 186
A = 513 + 186 = 699
Check the answer:
699 - 93 = 513 + 93 == 606
699 + 109 = (513 - 109) * 2 = 808