P is inversely proportional to Q₂

P ∝ $\frac{1}{{\mathrm{Q}}^2}$

Get rid of the proportionality sign (∝) by introducing a constant.

P = k x $\frac{1}{{\mathrm{Q}}^2}$

P = $\frac{\mathrm{k}}{{\mathrm{Q}}^2}$

When Q = 6, P = 2.25

$\frac{\mathrm{k}}{6^2}$ = 2.25

$\frac{\mathrm{k}}{36}$ = 2.25

Multiply both sides by 36

k = 2.25 x 36 = 81

P = $\frac{\mathrm{k}}{{\mathrm{Q}}^2}$

P = $\frac{81}{{\mathrm{Q}}^2}$

When Q = 3

P = $\frac{81}{3^2}$

P = $\frac{81}{9}$ = 9

The more the workers, the lesser the time.

Hence time (t) is inversely proportional to the number of workers (w).

t ∝ $\frac{1}{\mathrm{w}}$

Remove the proportionality by introducing a constant (k).

t = k x $\frac{1}{\mathrm{w}}$

Use the known information to solve for k

7 workers used 6 days.

6 = k x $\frac{1}{7}$

k = 6 x 7

The general equation is:

t = 6 x 7 x $\frac{1}{\mathrm{w}}$

t = $\frac{\mathrm{6\; x\; 7}}{\mathrm{w}}$

Calculate the time (t) for 2 workers.

w = 2

t = $\frac{\mathrm{6\; x\; 7}}{2}$ = 3 x 7 = 21

∴ It will take the two men 21 days to complete the work.

Ratios = 2 : 4 : 10

2 divides all.

Ratios = 1 : 2 : 5

Sum of ratios represents the total oranges shared.

The smallest ratio represents the least share.

Sum of ratios = 1 + 2 + 5 = 8

The smallest ratio = 1

If 8 = 32

1 = $\frac{\mathrm{1\; x\; 32}}{8}$ = 4

∴ The least share is 4