Question

.. If 2x and y vary inversely and x = 10 when y = 25, find x when y = 50.​

Answer 1

SOLUTION

GIVEN

• 2x and y vary inversely

• x = 10 when y = 25

TO DETERMINE

The value of x when y = 50

EVALUATION

Here it is given that 2x and y vary inversely

$\displaystyle \sf{2x \propto \: \frac{1}{y} }$

$\displaystyle \sf{ \implies \: 2x = \: \frac{k}{y} }$

$\displaystyle \sf{ \implies \: 2xy = k \: \: \: - - - - (1) }$

Where k is a non zero real number

Now x = 10 when y = 25

From Equation 1 we get

$\displaystyle \sf{ \: 2 \times 10 \times 25 = k}$

$\displaystyle \sf{ \implies \: k = 500}$

Equation 1 gives

$\displaystyle \sf{2xy = 500}$

Now for y = 50 we have

$\displaystyle \sf{ \implies \: 2 \times \: x \times 50 = 500}$

$\displaystyle \sf{ \implies \: 100x = 500}$

$\displaystyle \sf{ \implies \:x = 5}$

Hence the required value of x = 5

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