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Q.

I varies directly as m and I is equal to 5, when $m = \frac{2}{3} .$ What is the value of I when $m = \frac{16}{3}$ .

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a

40

b

50

c

60

d

70

answer is A.

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Detailed Solution

Concept: The fact that "I" varies in the same manner as "m" in the aforementioned question suggests that if "m" changes, then "I" will also change in the same proportion. The value of "I" will double if "m" doubles in value. I will also rise by 8 if "m" increases by 8. Now that we have the idea of direct proportion in our minds, we will convert all of the assertions into equations and find the value of the unknown.
I vary directly as m, or Im, in response to the query.

I = 5 given that m = \frac{2}{3} .

We must now determine the value of I if m = \frac{16}{3}, and we are aware that I is

\Rightarrow I = km— - (1)

(Calculating the values of "I" and "m") 5 = \frac{2}{3} k

k = \frac{15}{2}

Now, inserting k=

\frac{15}{2}

and m=

\frac{16}{3}

into equation (1) ,

I = \frac{15}{2} and \frac{16}{3} equals 40, and I equals . I has a value of 40 for m = \frac{16}{3}

Hence, the answer is

40

.
Thus, option 1 is correct.

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