Question

A is directly proportional to square of B and inversely proportional to C. Value of A, B and C are 12, 9 and 20 respectively. Find the value of A if B and C are 6 and 15 respectively​

Answer 1

SOLUTION

GIVEN

A is directly proportional to square of B and inversely proportional to C. Value of A, B and C are 12, 9 and 20 respectively.

TO DETERMINE

The value of A if B and C are 6 and 15 respectively

EVALUATION

Here it is given that A is directly proportional to square of B and inversely proportional to C

So by the given condition

$\displaystyle\sf{ \: A \propto \: {B}^{2} \: \: \: and \: \:A \propto \: \frac{1}{C} }$

$\displaystyle\sf{ \implies \: \:A \propto \: \frac{ {B}^{2} }{C} }$

$\displaystyle\sf{ \implies \: \:A = k\: \frac{ {B}^{2} }{C} } \: \: \: - - - (1)$

Where k is a non zero constant

Now A = 12 , B = 9 , C = 20

$\displaystyle\sf{ \implies \: \:12 = k\: \frac{ {9}^{2} }{20} }$

$\displaystyle\sf{ \implies \: \: k\: = \frac{12 \times 20}{ {9}^{2} } }$

Now it is given that B = 6 , C = 15

$\displaystyle\sf{ \implies \: \:A = k\: \frac{ {6}^{2} }{15} }$

$\displaystyle\sf{ \implies \: \:A = \frac{12 \times 20}{ {9}^{2} } \: \times \frac{ {6}^{2} }{15} }$

$\displaystyle\sf{ \implies \: \:A = \frac{16\times 36}{81 } \: }$

$\displaystyle\sf{ \implies \: \:A = \frac{64}{9 } \: }$

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