A quantity p is partly constant and partly varies inversely as a quantity q,given that p=10 when q is 1.5 and p=20 when q=1.25 find the value of p when q =0.5

To solve this problem, we can use the concept of inverse variation. Inverse variation means that as one variable increases, the other variable decreases and vice versa.

Let's denote the constant part of the quantity p as k.

We are given that p is partly constant and partly varies inversely as q, and we have two sets of values for p and q:

When q = 1.5, p = 10.
When q = 1.25, p = 20.

Using the concept of inverse variation, we can express the relationship between p and q as:

p = k/q

Now, we can solve for the value of k. Let's substitute the values from the first set of values:

10 = k/1.5

To isolate k, we can multiply both sides of the equation by 1.5:

10 * 1.5 = k

15 = k

Now that we have the value of k, we can substitute it into the equation to find the value of p when q = 0.5:

p = 15/0.5
p = 30

Therefore, when q = 0.5, the value of p is 30.

To find the value of p when q = 0.5, we can start by understanding the relationship between p and q.

We know that p is partly constant and partly varies inversely as q. This means that the value of p will have two components: a constant component and an inverse component.

Let's start by finding the constant component of p. We are given that p is equal to 10 when q is 1.5. So, we can write:

p = constant term + inverse term

If p = 10 and q = 1.5, we can substitute these values into the equation:

10 = constant term + inverse term

Next, let's find the inverse component of p. We know that p varies inversely with q, which means that p and q have an inverse relationship such that if q increases, p decreases and vice versa.

In mathematical terms, we can write this inverse relationship as:

p * q = k

where k is a constant. Rearranging this equation, we get:

p = k / q

Now, let's use the second set of given values to find the value of k. We are given that p is equal to 20 when q is 1.25. Substituting these values into the equation, we get:

20 = k / 1.25

To find the value of k, we multiply both sides of the equation by 1.25:

20 * 1.25 = k

k = 25

Now that we know the value of k, we can substitute it back into the first equation:

10 = constant term + inverse term

10 = constant term + 25 / 1.5

To find the constant term, we solve for it:

constant term = 10 - (25 / 1.5)
constant term = 10 - 16.67
constant term ≈ -6.67

Now, we have the constant term and the inverse term. We can use these to find the value of p when q = 0.5.

p = constant term + inverse term
p = -6.67 + (25 / 0.5)
p = -6.67 + 50
p ≈ 43.33

Therefore, the value of p when q = 0.5 is approximately 43.33.