# Pie Chart: Exercise-7

#### Overview:

 Questions and Answers Type: MCQ (Multiple Choice Questions). Main Topic: Data Interpretation. Data Interpretation Sub-topic: Pie Graph Questions and Answers. Number of Questions: 5 Questions with Solutions.

Directions: Study the following pie chart carefully and answer the questions given below it.

Distribution of areas (in acres) for growing various fruits.

1. If the total area goes up by 10%, and the area under grapes production goes up by 25%, then what will be the angle for grapes in the new pie chart?

1. $$40.25^0$$
2. $$43.05^0$$
3. $$45.45^0$$
4. $$42.15^0$$

Answer: (c) $$45.45^0$$

Solution: If the total area is $$x$$ then.

New total area $$= \frac{110 \ x}{100}$$ $$= \frac{11 \ x}{10}$$ The current area under grapes $$= \frac{40 \ x}{360}$$ $$= \frac{x}{9}$$ The new area under grapes $$= \left[\frac{125}{100} \times \frac{x}{9}\right]$$ $$= \frac{5x}{36}$$ New angle for grapes in the new pie chart.$$\left[\frac{\frac{5x}{36}}{\frac{11x}{10}} \times 360\right]$$ $$= \left[\frac{5x}{36} \times \frac{10}{11x} \times 360\right]$$ $$= 45.45^0$$

1. If the area under banana was five thousand acres then what was the area under pineapple (in thousand acres)?

1. 1.5 Thousand acres
2. 2.5 Thousand acres
3. 3.0 Thousand acres
4. 3.5 Thousand acres

Answer: (b) 2.5 Thousand acres

Solution: Let the total area is $$x$$ thousand acres.

Area under banana $$= \frac{80}{360} \times x$$ $$= \frac{2x}{9}$$ Area under pineapple $$= \frac{40}{360} \times x$$ $$= \frac{x}{9}$$ If $$\frac{2x}{9} = 5$$ thousand acres then $$x = 22.5$$ thousand acres.

Hence area under pineapple.$$= \frac{22.5}{9}$$ $$= 2.5 \ thousand \ acres$$

1. If the yield per acre of orange was 20% more than that of grapes, then the production of grapes is approximately what percent of that of orange?

1. 42 %
2. 40 %
3. 34 %
4. 32 %

Answer: (a) 42 %

Solution: Let the total area = $$x$$

then area under the orange $$= \frac{80x}{360}$$ $$= \frac{2x}{9}$$ Area under grapes $$= \frac{40x}{360}$$ $$= \frac{x}{9}$$ Let yield of grapes per acre = $$y$$ tons.

Then the yield of grapes per acre. $$= \frac{120y}{100}$$ $$= \frac{6y}{5} \ tons$$ Required percentage $$= \left[\frac{\frac{x}{9} \times y}{\frac{2x}{9} \times \frac{6y}{5}} \times 100\right] \ \%$$ $$= \left[\frac{xy}{9} \times \frac{45}{12xy} \times 100\right]$$ $$= 41.67 \ \%$$ $$\approx 42 \ \%$$

1. If the production of apple is three times that of pineapple, then what is the ratio between the yield per acre of apple and pineapple?

1. 2 : 3
2. 3 : 2
3. 3 : 4
4. 4 : 3

Answer: (d) 4 : 3

Solution: Let the total area = $$x$$

Then the area under the apple. $$= \frac{90x}{360}$$ $$= \frac{x}{4}$$ Area under pineapple $$= \frac{40x}{360}$$ $$= \frac{x}{9}$$ Let the production of the pineapple be $$P$$ tons.

Then the production of apple $$= 3P$$ tons.

The yield of apple per acre $$= \frac{3P}{\frac{x}{4}}$$ $$= \frac{12P}{x}$$ The yield of pineapple per acre $$= \frac{P}{\frac{x}{9}}$$ $$= \frac{9P}{x}$$ Required ratio $$= \left[\frac{\frac{12P}{x}}{\frac{9P}{x}}\right]$$ $$= \frac{12}{9}$$ $$= \frac{4}{3}$$ $$= 4 : 3$$

1. Which one fruit production area contributes to 25% of the total area under all fruits production?

1. Apple
2. Orange
3. Banana
4. Pineapple

Solution: For 25% of the total area, the angle should be $$90^0$$ and apple is the only fruit with $$90^0$$ angle on the pie chart. Hence the apple production area contributes to 25% of the total area.