Question

P and Q are two natural numbers. If both P and Q are increased by 5, the ratio becomes 3:5 and if both P and Q are decreased by 1, the ratio becomes 1:3. Find
P:Q.​

Answer 1

Answer:

according to question,

P+5 : Q+5= 3 : 5

=> P+5/Q+5=3/5

=> 5(P+5)=3(Q+5)

=> 5P+25=3Q+15

=> 5P=3Q+15-25

=> 5P=3Q-10

again,

P-1 : Q-1= 1 : 3

=> P-1/Q-1=1/3

=> 3(P-1)=1(Q-1)

=> 3P-3=Q-1

=> 3P=Q-1+3

=> 3P=Q+2

=> Q=3P-2

putting the value of Q in the above equation

5P=3Q-10

=> 5P=3(3P-2)-10

=> 5P=9P-6-10

=> 5P-9P= -16

=> -4P= -16

=> P= -16/-4

=> P=4

Q=3P-2

=3.4-2

=12-2

=10

so , P : Q = 4 : 10 = 2 : 5