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Three numbers are such that the second is as much lesser than the third as the first is lesser than the second. if the product of the two smaller numbers is 85 and the product of two larger numbers is 115 find the middle number?
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Three numbers are such that the second is as much lesser than the thir...
Given Information:
- Three numbers are such that the second is as much lesser than the third as the first is lesser than the second.
- Product of the two smaller numbers is 85.
- Product of the two larger numbers is 115.
Let's solve the problem step by step:
Step 1: Formulating the equations
Let the three numbers be x, y, and z.
According to the given information:
y = x - (z - y) = x - z + y
xy = 85
yz = 115
Step 2: Solving the equations
From the given information xy = 85 and y = x - z + y, we can substitute y = x - z + y in xy = 85:
x(x - z + y) = 85
x^2 - xz + xy = 85
x^2 - xz = 85 (i)
Similarly, from yz = 115:
z = 115/y
Substitute y = x - z + y in z = 115/y:
z = 115/(x - z + y)
z(x - z + y) = 115
xz - z^2 + yz = 115
xz - z^2 + 115 = 115
xz - z^2 = 0
z(x - z) = 0
z = x (ii)
Step 3: Finding the middle number
From equation (ii), we have z = x. Hence, the middle number is equal to the first number.
Therefore, the middle number is equal to the first number.
- Three numbers are such that the second is as much lesser than the third as the first is lesser than the second.
- Product of the two smaller numbers is 85.
- Product of the two larger numbers is 115.
Let's solve the problem step by step:
Step 1: Formulating the equations
Let the three numbers be x, y, and z.
According to the given information:
y = x - (z - y) = x - z + y
xy = 85
yz = 115
Step 2: Solving the equations
From the given information xy = 85 and y = x - z + y, we can substitute y = x - z + y in xy = 85:
x(x - z + y) = 85
x^2 - xz + xy = 85
x^2 - xz = 85 (i)
Similarly, from yz = 115:
z = 115/y
Substitute y = x - z + y in z = 115/y:
z = 115/(x - z + y)
z(x - z + y) = 115
xz - z^2 + yz = 115
xz - z^2 + 115 = 115
xz - z^2 = 0
z(x - z) = 0
z = x (ii)
Step 3: Finding the middle number
From equation (ii), we have z = x. Hence, the middle number is equal to the first number.
Therefore, the middle number is equal to the first number.
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Three numbers are such that the second is as much lesser than the third as the first is lesser than the second. if the product of the two smaller numbers is 85 and the product of two larger numbers is 115 find the middle number? for SSC CHSL 2025 is part of SSC CHSL preparation. The Question and answers have been prepared according to the SSC CHSL exam syllabus. Information about Three numbers are such that the second is as much lesser than the third as the first is lesser than the second. if the product of the two smaller numbers is 85 and the product of two larger numbers is 115 find the middle number? covers all topics & solutions for SSC CHSL 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three numbers are such that the second is as much lesser than the third as the first is lesser than the second. if the product of the two smaller numbers is 85 and the product of two larger numbers is 115 find the middle number?.
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