Question

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Answer 1

$\large\underline{\sf{Solution-}}$

Question:- 1 Based on Inverse Variation

The boxes are to be filled with mangoes in a heap. If 24 mangoes are put in a box, then 27 boxes are required. If 36 mangoes are filled in a box, how many boxes will be required?

ANSWER : -

Now, in this question, we have given that 24 mangoes to be put in a box and total 27 boxes required. Now, If number of mangoes in a box is increased, then the number of boxes decreases.

This implies, the number of mangoes to be filled in the box and the number of boxes are in inversely proportional to each other.

Let assume that

Number of boxes required to fill 36 mangoes in a box be x.

So,

$\begin{gathered}\boxed{\begin{array}{c|c} \bf Number \: of \: mangoes & \bf Number \: of \: boxes \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 24 & \sf 27 \\ \\ \sf 36 & \sf x \end{array}} \\ \end{gathered}$

Now, By using Law of inverse Variation

$\rm \: 24 \times 27 = 36 \times x$

$\rm \: 24 \times 3 = 4 \times x$

$\rm \: 6 \times 3 = x$

$\rm\implies \:x = 18$

So, it means 18 boxes required to fill 27 mangoes in each box.

Question :- 2 Based on Direct Variation

If the cost of 10 kg mangoes is Rs 1000, what is the cost of 5 kg of mangoes ?

ANSWER :-

As it is given that, Cost of 10 kg of mangoes is Rs 1000 and we have to find the cost of 5 kg of mangoes.

As quantity of mangoes decreases, so price also decreases.

It means, quantity and price varies directly proportional to each other.

Let assume that price of 5 kg mangoes be x.

So,

$\begin{gathered}\boxed{\begin{array}{c|c} \bf Quantity \: of \: mangoes & \bf Price \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 10 & \sf 1000 \\ \\ \sf 5 & \sf x \end{array}} \\ \end{gathered}$

So, By Law of Direct variation, we have

$\rm \: \dfrac{10}{1000} = \dfrac{5}{x}$

$\rm \: \dfrac{1}{100} = \dfrac{5}{x}$

$\rm\implies \:x = 500$

So, price of 5 kg mangoes = Rs 500