The three number are in the ratio of 3:7:9. If 5 subtracted from the s...
Let the three numbers which are in the ratio 3:7:9 be 3x,7x and 9x.
Now, on subtracting 5 from the second number, we get the
Three numbers as 3x, 7x-5 and 9x
Since, these numbers are in AP, therefore, we have
2(7x-5) = 3x+9x
= 14x-10 = 12x
= 2x=10
= x=5
Hence, the three original numbers are 3x =15, 7x=35 and 9x =45
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The three number are in the ratio of 3:7:9. If 5 subtracted from the s...
Given Information:
The three numbers are in the ratio of 3:7:9.
To Find:
The number obtained when 5 is subtracted from the second number, and whether the resulting number forms an arithmetic progression (AP).
Solution:
Let's assume the three numbers in the ratio of 3:7:9 as 3x, 7x, and 9x.
Step 1: Expressing the Numbers
Express the three numbers in terms of x:
- The first number is 3x.
- The second number is 7x.
- The third number is 9x.
Step 2: Subtracting 5 from the Second Number
Subtracting 5 from the second number gives us: 7x - 5.
Step 3: Checking if the Result Forms an AP
To check if the resulting number forms an arithmetic progression, we need to compare the difference between the second and first numbers with the difference between the third and second numbers.
The difference between the second and first numbers is (7x - 5) - 3x = 4x - 5.
The difference between the third and second numbers is 9x - (7x) = 2x.
If these two differences are equal, then the resulting numbers form an AP.
Step 4: Equating the Differences
Setting the two differences equal, we get:
4x - 5 = 2x.
Step 5: Solving the Equation
Solving the equation for x:
4x - 5 = 2x
4x - 2x = 5
2x = 5
x = 5/2
Step 6: Finding the Numbers
Now that we have the value of x, we can substitute it back into the expressions for the three numbers.
The first number is 3x = 3 * (5/2) = 15/2.
The second number is 7x = 7 * (5/2) = 35/2.
The third number is 9x = 9 * (5/2) = 45/2.
Therefore, the three numbers in the ratio of 3:7:9 are 15/2, 35/2, and 45/2.
Conclusion:
The number obtained when 5 is subtracted from the second number is 35/2 - 5 = 35/2 - 10/2 = 25/2.
The resulting number, 25/2, does not form an arithmetic progression with the other two numbers.
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