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.
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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.
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