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A farmer deposited some money (principal) at a simple interest rate. We are given the total amount after 2 years and the interest rate. Calculate the principal amount.

Mathematics

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Question 18a)
To express the sector for "Others" as a percentage, we first need its angle. Based on the calculation shown next to the question, we assume the angle for "Others" is 110∘110^\circ.

Step 1: Identify the angle for the sector "Others".
The angle for "Others" is 110∘110^\circ.

Step 2: Calculate the percentage.
The percentage is found by dividing the sector angle by the total angle in a circle (360∘360^\circ) and multiplying by 100%100\%.

Percentage for Others=Angle of sectorTotal angle×100%\text{Percentage for Others} = \frac{\text{Angle of sector}}{\text{Total angle}} \times 100\% Percentage for Others=110∘360∘×100%\text{Percentage for Others} = \frac{110^\circ}{360^\circ} \times 100\%

Step 3: Perform the calculation.

Percentage for Others=1136×100%\text{Percentage for Others} = \frac{11}{36} \times 100\% Percentage for Others=110036%\text{Percentage for Others} = \frac{1100}{36}\% Percentage for Others=2759%\text{Percentage for Others} = \frac{275}{9}\% Percentage for Others≈30.555...%\text{Percentage for Others} \approx 30.555...\%

Rounding to one decimal place:

Percentage for Others≈30.6%\text{Percentage for Others} \approx \boxed{30.6\%}

Part 19

The table showing marks obtained by P.7 pupils is incomplete. The last column for "Marks" and "No. of pupils" is cut off. Without the complete data, it is not possible to accurately determine the value of 'w' or the median score.

Part 20· 3 steps

A farmer deposited some money (principal) at a simple interest rate. We are given the total amount after 2 years and need to find the principal.

Given:

  • Total Amount (A) = sh. 72000
  • Interest Rate (R) = 10% per annum
  • Time (T) = 2 years

We use the formula for the total amount (A) with simple interest:

A=P(1+R×T100)A = P \left(1 + \frac{R \times T}{100}\right)

Where P is the principal.

  1. Substitute the given values into the formula.

    72000=P(1+10×2100)72000 = P \left(1 + \frac{10 \times 2}{100}\right)
  2. Simplify the expression inside the parenthesis.

    72000=P(1+20100)72000 = P \left(1 + \frac{20}{100}\right) 72000=P(1+15)72000 = P \left(1 + \frac{1}{5}\right) 72000=P(55+15)72000 = P \left(\frac{5}{5} + \frac{1}{5}\right) 72000=P(65)72000 = P \left(\frac{6}{5}\right)
  3. Solve for P.

    P=72000×56P = 72000 \times \frac{5}{6} P=72000×56P = \frac{72000 \times 5}{6} P=12000×5P = 12000 \times 5 P=60000P = 60000

    The principal amount deposited was sh. 60000.

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