Question

Three numbers are in ratio 1 : 3 : 10. If 20 is subtracted from the largest number, the numbers form a geometric sequence. Determine the three numbers.

Answer 1

Answer:

20,60 and 200

Step-by-step explanation:

Let's assume that the numbers are x, 3x and 10x respectively.

After subtracting 20 from the largest number(10x), the numbers form a geometric sequence(GP).

As per the property of GP, if three numbers a,b,c are in GP then b²= ac

Therefore, (3x)² = x*(10x-20)

==> 9x² = 10x² - 20x

==> 10x²-9x²-20x= 0

==> x²-20x = 0

==> x(x-20) = 0

==> x= 0 or x= 20

Considering x= 0 will make all three numbers zero hence ignoring it.

The correct value of x is 20 and hence the numbers are

20,

20*3 = 60 and

20*10 = 200

20,60 and 200 respectively.