12 years ago, age of P was 3 times the age of Q.After 12 years,ratio of ages of Q to P will be 2:3.What is the present age of P?54 years36 years24 years144 years
Question
12 years ago, age of P was 3 times the age of Q.After 12 years,ratio of ages of Q to P will be 2:3.What is the present age of P?54 years36 years24 years144 years
Solution
Let's denote the present age of P as P and the present age of Q as Q.
From the problem, we know that:
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12 years ago, P was 3 times as old as Q. This can be written as: P - 12 = 3(Q - 12)
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In 12 years, the ratio of Q's age to P's age will be 2:3. This can be written as: (Q + 12) / (P + 12) = 2/3
We can solve these two equations to find the values of P and Q.
Let's start with the first equation:
P - 12 = 3Q - 36 P = 3Q - 24
Now, let's substitute P in the second equation:
(Q + 12) / (3Q - 24 + 12) = 2/3 3(Q + 12) = 2(3Q - 12) 3Q + 36 = 6Q - 24 3Q = 60 Q = 20
Substitute Q = 20 into the equation P = 3Q - 24, we get:
P = 3*20 - 24 P = 60 - 24 P = 36
So, the present age of P is 36 years.
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