Question 57

The average of four consecutive numbers A, B, C and D respectively is 49.5. What is the product of B and D?

Solution

Since the ages of A, B, C, D are consecutive

Let the ages of A, B, C, D be n, n+1,n+2,n+3

$$\frac{n+n+1+n+2+n+3}{4} = 49.5$$

4n+6 = 49.5*4 = 198

4n = 192

n = 48

Ages of A, B, C, D = 48, 49, 50 ,51

Product of ages of B and D = 49*51 = (50-1)(50+1) =$$50^2-1$$ = 2500-1 = 2449.  


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