Use the pie-chart below to answer the questions that follow. (a) Find the value of Y. (b) If chicken and Turkeys are 517, find the total number of birds.

The fraction of Turkeys in the pie chart is $\frac{1}{3}$. The total angle in a circle is $360^\circ$.

$$\text{Angle for Turkeys} = \frac{1}{3} \times 360^\circ = 120^\circ$$

The sum of all angles in a pie chart is $360^\circ$.

$$100^\circ (\text{Chicken}) + 120^\circ (\text{Turkeys}) + Y (\text{Pigeons}) = 360^\circ$$ $$220^\circ + Y = 360^\circ$$ $$Y = 360^\circ - 220^\circ$$ $$Y = 140^\circ$$

The value of Y is $\boxed{140^\circ}$.

Angle for Chicken $= 100^\circ$.
Angle for Turkeys $= 120^\circ$ (from part a).

$$\text{Total angle for Chicken and Turkeys} = 100^\circ + 120^\circ = 220^\circ$$

We are given that the number of Chicken and Turkeys is 517, which corresponds to $220^\circ$. Let the total number of birds be $N$. The total angle is $360^\circ$.

$$\frac{\text{Number of Chicken and Turkeys}}{\text{Total number of birds}} = \frac{\text{Angle for Chicken and Turkeys}}{\text{Total angle}}$$ $$\frac{517}{N} = \frac{220^\circ}{360^\circ}$$ $$N = \frac{517 \times 360}{220}$$ $$N = \frac{517 \times 18}{11}$$ $$N = 47 \times 18$$ $$N = 846$$

The total number of birds is $\boxed{846}$.

24.

Cost of 30 watermelons $= 30 \times \text{sh. } 10,000 = \text{sh. } 300,000$.
Transportation cost $= \text{sh. } 45,000$.

$$\text{Total Cost} = \text{sh. } 300,000 + \text{sh. } 45,000 = \text{sh. } 345,000$$

Selling price per good watermelon $= \text{sh. } 12,000$.
Tax per good watermelon $= 5\% \text{ of sh. } 10,000 = 0.05 \times \text{sh. } 10,000 = \text{sh. } 500$.

$$\text{Net selling price per good watermelon} = \text{sh. } 12,000 - \text{sh. } 500 = \text{sh. } 11,500$$

Let $x$ be the number of spoilt watermelons.
Number of good watermelons $= 30 - x$.
Total Revenue $= (30 - x) \times \text{sh. } 11,500$.
Loss = Total Cost - Total Revenue.
Given Loss $= \text{sh. } 46,000$.

$$\text{sh. } 46,000 = \text{sh. } 345,000 - (30 - x) \times \text{sh. } 11,500$$

$$11,500(30 - x) = 345,000 - 46,000$$ $$11,500(30 - x) = 299,000$$ $$30 - x = \frac{299,000}{11,500}$$ $$30 - x = \frac{2990}{115}$$ $$30 - x = 26$$ $$x = 30 - 26$$ $$x = 4$$

The number of watermelons that got spoilt during transportation is $\boxed{4}$.