Video Explanation

Text Explanation

Given: the average (arithmetic mean) of b and c is 5. Therefore,

Similarly, it’s given that the average of c and d is 10. Therefore,

Notice that we have two equations with three unknowns and therefore we cannot find the values of b, c and d individually.

We need b − d and therefore c needs to be eliminated. One way of doing this is to isolate c in both equations and set them equal.

From the first equation we have

c = 10 − b

From the second equation we have

c = 20 − d

Therefore,

10 − b = 20 − d  

As we need b − d, we want to take the b to the other side by adding b to both sides that gives

10 = 20 + b − d

Finally,

Subtracting 20 from both sides we get

b − d = 10 − 20 = −10.

Alternatively, we could subtract the two equations to get rid of c. As we need b (or +b) and −d, we should subtract the second equation from the first.

(b + c) − (c + d) = 10 − 20

Or, b + c − c − d = −10

Or, b − d = −10

Answer: (C)