1.

If x and y varies inversely as each other and x= 8 when y=10 find y when x =5

Answer»

rong>SOLUTION

GIVEN

  • x and y varies inversely as each other and x = 8 when y=10

TO DETERMINE

The value of y when x =5

EVALUATION

Here it is given that x and y varies inversely as each other

\displaystyle \sf{x \propto \:  \frac{<klux>1</klux>}{y} }

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

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

Where k is a non zero real number

Now x = 8 when y = 10

We get from equation 1

\displaystyle \sf{ \implies \: (8 \times 10) = k }

\displaystyle \sf{ \implies \:  k = 80 }

Equation 1 gives

\displaystyle \sf{ \implies \: xy = 80}

Now for x = 5 we have

\displaystyle \sf{ \implies \: 5y = 80}

\displaystyle \sf{ \implies \: y = 16}

FINAL ANSWER

Hence the required value of y = 16

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