The ratio of p:q is 3:2.
Step-by-step explanation:
It is given that,
When you subtract 15 from p and subtract 15 from q, the answers are in ratio 2 : 1.
The equation can be framed as,
(p - 15)/(q - 15) = 2/1 ---------- equation (1)
p - 15 = 2(q - 15)
p - 15 = 2q - 30
p = 2q - 15 --------equation (2)
When you add 30 to p and add 30 to q the answers are in the ratio 5 : 4.
(p + 30)/(q + 30) = 5/4 --------- equation (3)
4(p + 30) = 5(q + 30)
4p + 120 = 5q + 150
4p = 5q + 30 ---------equation (4)
Substitute eq (2) p = 2q - 15 in eq (4),
⇒ 4 (2q - 15) = 5q + 30
⇒ 8q - 60 = 5q + 30
⇒ 3q = 90
⇒ q = 90/3
⇒ q = 30
Solving for p, substitute q=30 in eq (2),
⇒ p = 2q - 15
⇒ p = 2(30) - 15
⇒ p = 60-15
⇒ p = 45
To find the ratio of p : q,
we found that, p= 45 and q= 30
Therefore, p/q = 45/30 ⇒ 3/2
∴ The ratio of p:q is 3:2.
The value of p and q is 45 and 30 respectively equivalent to 3 : 2 in it's simplest form
Given:
p - 15 / q - 15 = 2/1
cross product
(p - 15)1 = (q - 15)2
p - 15 = 2q - 30
p - 2q = -30 + 15
p - 2q = - 15 (1)
p + 30 / q + 30 = 5/4
cross product
(p + 30) 4 = (q + 30) 5
4p + 120 = 5q + 150
4p - 5q = 150 - 120
4p - 5q = 30 (2)
p - 2q = - 15 (1)
4p - 5q = 30 (2)
multiply (1) by 4
4p - 8q = -60 (3)
4p - 5q = 30 (2)
subtract (2) from (3)
-8q - (-5q) = -60 - 30
-8q + 5q = -90
-3q = - 90
q = -90/-3
q = 30
substitute into p - 2q = - 15
p - 2(30) = -15
p - 60 = -15
p = -15 + 60
p = 45
Therefore, the ratio of p and q is 45 : 30
= 3 : 2
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