# There are two buildings P and Q. If 15 persons are sent from P to Q, then the number of persons in each building is the same. If 20 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?

Aptitude Solved Problems

1. There are two buildings P and Q. If 15 persons are sent from P to Q, then the number of persons in each building is the same. If 20 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?

Explanation:
Let the number of persons in building P = p
and the number of persons in building Q = q
If 15 persons are sent from P to Q,
Then the number of persons in each building is the same
( p - 15 ) = ( q + 15 )
( p - q ) = 30 ...... ( Eqn 1 )
If 20 persons are sent from Q to P,
Then the number of persons in P is double the number of persons in Q
2 ( q - 20) = ( p + 20 )
( 2q - 40 ) = p + 20
( 2q - p ) = 60 ...... ( Eqn 2 )
( Eqn 1 ) + ( Eqn 2 )
We get, q = 90
From Eqn 1,
( p - q ) = 30
p = ( 30 + q )
p = ( 30 + 90 )
= 120
∴ Building P has 120 persons.

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