CBSE Class 6 Mathematics Revision Worksheet Set 08

Question 1. There are 50 persons in an office. If the numbers of females is 20 and remaining are males, find the ratio of:
a. Number of females to number of males.
b. Number of males to tatal number of persons.
Answer:
Total number of persons = 50
Number of females = 20
Number of males = Total persons - Number of females
Number of males = 50 - 20 = 30

a. Ratio of number of females to number of males:
\(\text{Ratio} = \frac{20}{30} = \frac{2}{3}\) or \(2:3\)

b. Ratio of number of males to total number of persons:
\(\text{Ratio} = \frac{30}{50} = \frac{3}{5}\) or \(3:5\)
In simple words: First find the number of males by subtracting females from the total, then write the required values as fractions in their simplest form.
Exam Tip: Always reduce ratios to their lowest terms and check that quantities are in the same unit before comparing.

Question 2. Find the ratio of the following:
a. 50 cm to 2 m
b. 3 lts to 200 ml
c. 400 m to 1 km
Answer:
a. Convert both quantities into centimeters: 2 m = \(2 \times 100\) cm = 200 cm.
Ratio = \(\frac{50}{200} = \frac{1}{4}\) or \(1:4\)

b. Convert both quantities into milliliters: 3 lts = \(3 \times 1000\) ml = 3000 ml.
Ratio = \(\frac{3000}{200} = \frac{30}{2} = \frac{15}{1}\) or \(15:1\)

c. Convert both quantities into meters: 1 km = 1000 m.
Ratio = \(\frac{400}{1000} = \frac{4}{10} = \frac{2}{5}\) or \(2:5\)
In simple words: Convert both quantities to the same unit first, then write them as a fraction and simplify.

Exam Tip: Never find a ratio between different units directly; always convert them to a common unit first.

Question 3. Find a, b, c:
\(20 / 24 = a / 6 = 15 / b = 30 / c\)
Answer:
First, simplify the given fraction: \(\frac{20}{24} = \frac{5}{6}\)

Now, equate each part to \(\frac{5}{6}\):
1. For a:
\(\frac{a}{6} = \frac{5}{6}\)
\(a = 5\)

2. For b:
\(\frac{15}{b} = \frac{5}{6}\)
\(5b = 15 \times 6\)
\(5b = 90\)
\(b = \frac{90}{5} = 18\)

3. For c:
\(\frac{30}{c} = \frac{5}{6}\)
\(5c = 30 \times 6\)
\(5c = 180\)
\(c = \frac{180}{5} = 36\)

Thus, \(a = 5\), \(b = 18\), and \(c = 36\).
In simple words: Use equivalent fractions by cross-multiplication or by finding the multiplier for numerators and denominators.

Exam Tip: Cross-multiplication (\(ad = bc\)) is a foolproof method for solving proportions with unknown variables.

Question 4. Determine if they are in proportion
a. 2:4 :: 15:30
b. 18:24 :: 27:36
Answer:
a. Product of extremes = \(2 \times 30 = 60\)
Product of means = \(4 \times 15 = 60\)
Since Product of extremes = Product of means, 2:4 and 15:30 are in proportion.

b. Product of extremes = \(18 \times 36 = 648\)
Product of means = \(24 \times 27 = 648\)
Since Product of extremes = Product of means, 18:24 and 27:36 are in proportion.
In simple words: Check if the product of the first and last numbers equals the product of the two middle numbers.

Exam Tip: Four numbers \(a, b, c, d\) are in proportion if \(a \times d = b \times c\).

Question 5. If a car travels 48 km in 8 hours, how much will it travel in 11 hours.
Answer:
Distance traveled in 8 hours = 48 km
Distance traveled in 1 hour = \(\frac{48}{8} = 6\) km
Distance traveled in 11 hours = \(6 \times 11 = 66\) km
In simple words: Find the distance covered in 1 hour first (unitary method), then multiply it by 11.

Exam Tip: Always find the value of a single unit first before calculating for multiple units.

Question 6. Find the distance travelled by Rahul if he takes 2 rounds of a square park of side 35m.
Answer:
Side of the square park = 35 m
Perimeter of the square park = \(4 \times \text{side} = 4 \times 35 = 140\) m
Distance covered in 1 round = Perimeter = 140 m
Distance covered in 2 rounds = \(2 \times 140 = 280\) m
In simple words: Multiply the perimeter of the square by 2 to find the total distance for two rounds.

Exam Tip: Perimeter represents the total boundary length. Walking rounds around a park means multiplying the perimeter by the number of rounds.

Question 7. Area of rectangle is 36 sq m. If the length of the rectangle is 12 m, find its breadth.
Answer:
Area of rectangle = 36 sq m
Length \((l)\) = 12 m
Area = \(\text{Length} \times \text{Breadth}\)
\(36 = 12 \times \text{Breadth}\)
Breadth = \(\frac{36}{12} = 3\) m
In simple words: Divide the given area by the length to get the breadth.

Exam Tip: Always include the correct linear units (like m) for dimensions and square units (like sq m) for areas.

Question 8. Fill in the blanks:
a. Area of rectangle = _____
b. Perimeter of square = _____
c. Area of square = _____
d. Perimeter of rectangle = _____
Answer:
a. Area of rectangle = \(\text{Length} \times \text{Breadth}\)
b. Perimeter of square = \(4 \times \text{Side}\)
c. Area of square = \(\text{Side} \times \text{Side}\)
d. Perimeter of rectangle = \(2(\text{Length} + \text{Breadth})\)
In simple words: Memorize the standard formulas for perimeter and area of basic geometric shapes.

Exam Tip: Keep formula sheets handy and revise them regularly before geometry exams.

Question 9. Find the perimeter of the following:
Answer:
a. Sum of all outer boundary lengths of figure (a):
Perimeter = \(2 + 5 + 1 + 4 + 4 + 1 + 5 = 22\) cm

b. Sum of all outer boundary lengths of figure (b):
Perimeter = \(3 + 1 + 1 + 2 + 1 + 1 + 3 + 4 + 3 + 1 + 1 + 2 + 1 + 1 + 3 + 4 = 32\) cm
In simple words: Add up the lengths of all outer boundary segments shown in the figures.

Exam Tip: Be careful not to add internal dividing lines when calculating the perimeter of a composite figure.

Question 10. A girl is asked to collect data for size of shoes of 40 students in her class VI. Her findings are recorded as follows:
5 4 7 5 6 7 6 5 6 6 5 4 5 6 8 7 4 6 5 6 4
6 5 7 6 7 5 7 6 7 4 8 7 6 6 7 5 6 5 7 6
a. Prepare a Tally marks table.
b. Represent the tally marks table on graph paper by making bar graph.
Answer:
a. Let us count the frequency of each shoe size (ranging from 4 to 8):
- Size 4: 4 times
- Size 5: 11 times
- Size 6: 13 times
- Size 7: 9 times
- Size 8: 3 times
Total frequency = \(4 + 11 + 13 + 9 + 3 = 40\)

Tally Marks Table:

b. Bar Graph Representation:
In simple words: Count each data item carefully using tally marks, find their total frequencies, and draw rectangular bars proportional to each frequency on graph axes.
Exam Tip: Always double-check that the sum of all individual frequencies equals the total given number of observations (40 students).