Question

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

• A. 16
• B. 18
• C. 8
• D. 9

Answer 1

The correct option is B 18

Let x represent the number of apples in each box and y represent the total number of boxes required.
The number of apples in each box are varying inversely with the total number of boxes.
$\therefore x\alpha \left(\frac{1}{y}\right)$
$\therefore x=k\times \left(\frac{1}{y}\right)$ where, k is the constant of variation,

$\therefore x\times y=k$ ...(i)

If 24 apples are put in a box then 27 boxes are needed. i.e., when x = 24, y = 27 in (i), we get
$x\times y=k\therefore 24\times 27=k\therefore k=648$

Substituting k = 648 in (i),

we get $x\times y=648$ ...(ii)

This is the equation of variation. Now, we have to find number of boxes needed when, 36 apples are filled in each box, i.e., when x = 36, y = ?

$\therefore$ Substituting x = 36 in (ii),
we get $x\times y=648\therefore 36\times y=648\therefore y=\frac{648}{36}\therefore y=18.$