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A varies directly with difference of B and C. B varies directly with M and C varies directly with √M. If M = 4 then A = 18 and when M = 9 then A = 42. Find the value of M when A = 4.

A varies directly with difference of B and C. B varies directly with M and C varies directly with √M. If M = 4 then A = 18 and when M = 9 then A = 42. Find the value of M when A = 4. Correct Answer 1

Given:

⇒ A = K(B - C)......(K is a constant)

⇒ B = k(M)......(k is a constant)

⇒ C = n(√M)......(n is a constant)

Calculation:

⇒ A = K(kM - √M)

⇒ A = (PM - Q√M)......( P = Kk and Q = Kn)

Then,

⇒ 18 = 4P - 2Q

⇒ 42 = 9P - 3Q

Solving,

⇒ P = 5 and Q = 1

Then,

⇒ 4 = 5M - 1 × √M

⇒ M = 1......(by trial and error)

∴ Required value of M = 1

Related Questions

A varies directly with the sum of B and C. B varies directly with D and C varies directly with D2. If D = 2 then A = 16 and if D = 4 then A = 56. What is the value of A when D = 3?
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