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The sum of the reciprocals of the ages of two brothers Mahesh Babu and Ravi Teja is five times the difference of the reciprocals of their ages. If the ratio of the product of their ages to the sum of their ages is 14.4 : 1, find their ages.
- a)36 and 24 yr
- b)24 and 20 yr
- c)18 and 15 yr
- d)12 and 9 yr
Correct answer is option 'A'. Can you explain this answer?
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The sum of the reciprocals of the ages of two brothers Mahesh Babu and...
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The sum of the reciprocals of the ages of two brothers Mahesh Babu and...
( 1/x+1/y ) = 5 ( 1/x - 1/y)
x+y/xy = 5( y-x/xy)
x+y = 5y - 5x
6x= 4y or 2y=3x or y= 1.5 x
xy/ x+y = 14.4/1
14.4( x+y) = xy
14.4( 2.5x) = 1.5x^2
72 * 5 = 15 x
x= 24
y= 1.5 x
y= 36
x+y/xy = 5( y-x/xy)
x+y = 5y - 5x
6x= 4y or 2y=3x or y= 1.5 x
xy/ x+y = 14.4/1
14.4( x+y) = xy
14.4( 2.5x) = 1.5x^2
72 * 5 = 15 x
x= 24
y= 1.5 x
y= 36
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The sum of the reciprocals of the ages of two brothers Mahesh Babu and...
Let's assume the ages of Mahesh Babu and Ravi Teja as x and y years respectively.
Given information:
1. The sum of the reciprocals of their ages is five times the difference of the reciprocals of their ages:
1/x + 1/y = 5(1/y - 1/x)
2. The ratio of the product of their ages to the sum of their ages is 14.4:1:
xy / (x + y) = 14.4/1
To solve this problem, we will use the given information to form a system of equations and solve for the values of x and y.
Equation 1: 1/x + 1/y = 5(1/y - 1/x)
To simplify this equation, we can multiply through by xy to eliminate the denominators:
y + x = 5(y - x)
Equation 2: xy / (x + y) = 14.4/1
To simplify this equation, we can cross-multiply:
xy = 14.4(x + y)
Now, let's solve the system of equations:
Step 1: Simplify Equation 1:
y + x = 5y - 5x
6x = 4y
3x = 2y
Step 2: Substitute the value of x from Equation 2 into Equation 1:
3x = 2y
3(14.4(x + y)) = 2y
43.2(x + y) = 2y
43.2x + 43.2y = 2y
43.2x = -41.2y
x = -41.2/43.2y
x ≈ -0.9537y
Since age cannot be negative, we can ignore the negative solution and consider the positive values.
Step 3: Substitute the value of x in terms of y into Equation 2:
xy = 14.4(x + y)
y(-0.9537y) = 14.4(-0.9537y + y)
-0.9537y² = 14.4(0.0463y)
-0.9537y² = 0.668y
y = -0.668/0.9537
y ≈ -0.7005
Again, age cannot be negative, so we ignore the negative solution and consider the positive values.
Therefore, the ages of Mahesh Babu and Ravi Teja are approximately x = 0.9537y and y = 0.7005 years.
To find the exact ages, we can multiply the approximate values by their common denominator, which is 10000:
x ≈ 0.9537y ≈ 0.9537(0.7005) ≈ 6660.405 years ≈ 6660 years
y ≈ 0.7005 years ≈ 7005 years
So, the ages of Mahesh Babu and Ravi Teja are approximately 6660 years and 7005 years respectively.
Given information:
1. The sum of the reciprocals of their ages is five times the difference of the reciprocals of their ages:
1/x + 1/y = 5(1/y - 1/x)
2. The ratio of the product of their ages to the sum of their ages is 14.4:1:
xy / (x + y) = 14.4/1
To solve this problem, we will use the given information to form a system of equations and solve for the values of x and y.
Equation 1: 1/x + 1/y = 5(1/y - 1/x)
To simplify this equation, we can multiply through by xy to eliminate the denominators:
y + x = 5(y - x)
Equation 2: xy / (x + y) = 14.4/1
To simplify this equation, we can cross-multiply:
xy = 14.4(x + y)
Now, let's solve the system of equations:
Step 1: Simplify Equation 1:
y + x = 5y - 5x
6x = 4y
3x = 2y
Step 2: Substitute the value of x from Equation 2 into Equation 1:
3x = 2y
3(14.4(x + y)) = 2y
43.2(x + y) = 2y
43.2x + 43.2y = 2y
43.2x = -41.2y
x = -41.2/43.2y
x ≈ -0.9537y
Since age cannot be negative, we can ignore the negative solution and consider the positive values.
Step 3: Substitute the value of x in terms of y into Equation 2:
xy = 14.4(x + y)
y(-0.9537y) = 14.4(-0.9537y + y)
-0.9537y² = 14.4(0.0463y)
-0.9537y² = 0.668y
y = -0.668/0.9537
y ≈ -0.7005
Again, age cannot be negative, so we ignore the negative solution and consider the positive values.
Therefore, the ages of Mahesh Babu and Ravi Teja are approximately x = 0.9537y and y = 0.7005 years.
To find the exact ages, we can multiply the approximate values by their common denominator, which is 10000:
x ≈ 0.9537y ≈ 0.9537(0.7005) ≈ 6660.405 years ≈ 6660 years
y ≈ 0.7005 years ≈ 7005 years
So, the ages of Mahesh Babu and Ravi Teja are approximately 6660 years and 7005 years respectively.
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