The boxes are to be filled with apples in a heap. If 24 apples are put

1.	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?
Answer» 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. ∴ x ∝ (1/y) ∴ x = k x (1/y) where, k is the constant of variation, ∴ x × y = k …(i) If 24 apples are put in a box then 27 boxes are needed. i.e., when x = 24, y = 27 ∴ Substituting x = 24 and y = 27 in (i), we get x × y = k ∴ 24 × 27 = k ∴ k = 648 Substituting k = 648 in (i), we get x × y = k ∴ x × 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 = ? ∴ Substituting x = 36 in (ii), we get x × y = 648 ∴ 36 × y = 648 ∴ y = 648/36 ∴ y = 18 ∴ If 36 apples are filled in a box then 18 boxes are required.

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?

Answer»

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.

∴ x ∝ (1/y)

∴ x = k x (1/y)

where, k is the constant of variation,

∴ x × y = k …(i)

If 24 apples are put in a box then 27 boxes are needed.

i.e., when x = 24, y = 27

∴ Substituting x = 24 and y = 27 in (i), we get

x × y = k

∴ 24 × 27 = k

∴ k = 648

Substituting k = 648 in (i), we get

x × y = k

∴ x × 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 = ?

∴ Substituting x = 36 in (ii), we get

x × y = 648

∴ 36 × y = 648

∴ y = 648/36

∴ y = 18

∴ If 36 apples are filled in a box then 18 boxes are required.