Finding Common Ground — Class 7 Mathematics NCERT Solutions (Free)
Free step-by-step NCERT solutions for Class 7 Mathematics chapter "Finding Common Ground" — 8 important questions with detailed answers for CBSE board exam preparation.
TL;DR: Free step-by-step NCERT solutions for Class 7 Mathematics chapter "Finding Common Ground" — 8 important questions with detailed answers for CBSE board…
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Key Questions Covered:
- Define ratio and proportion. Explain the difference with examples.
- Simplify the ratio 24:36 and verify if 24:36 is equal to 2:3.
- If the ratio of two numbers is 3:5 and their sum is 40, find the numbers.
- What is a percentage? Convert 3/8 to percentage and 45% to a fraction.
- If a shirt costs Rs. 800 and a discount of 25% is given, what is the selling …
- What is simple interest? Calculate simple interest on Rs. 5000 at 8% per annu…
- + 2 more questions in the full chapter
Solutions Summary:
| Question | Status |
|---|---|
| Define ratio and proportion. Explain the difference with … | ✓ Solved |
| Simplify the ratio 24:36 and verify if 24:36 is equal to … | ✓ Solved |
| If the ratio of two numbers is 3:5 and their sum is 40, f… | ✓ Solved |
| What is a percentage? Convert 3/8 to percentage and 45% t… | ✓ Solved |
| If a shirt costs Rs. 800 and a discount of 25% is given, … | ✓ Solved |
| What is simple interest? Calculate simple interest on Rs.… | ✓ Solved |
Showing 6 of 8 questions
Q1: Define ratio and proportion. Explain the difference with examples.
Ratio:
A ratio is a comparison of two quantities of the same kind using division.
Ratio of a to b is written as a:b or a/b (read as "a to b").
Both quantities must have the same units.
Example:
If there are 5 boys and 3 girls in a class:
Ratio of boys to girls = 5:3 (read as "5 to 3")
Ratio of girls to boys = 3:5
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Proportion:
A proportion is an equation stating that two ratios are equal.
If a:b = c:d, then a/b = c/d, written as a:b::c:d (read as "a is to b as c is ...
Q2: Simplify the ratio 24:36 and verify if 24:36 is equal to 2:3.
Simplifying the ratio 24:36:
Step 1: Find the GCD (Greatest Common Divisor) of 24 and 36
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Common factors: 1, 2, 3, 4, 6, 12
GCD = 12
Step 2: Divide both terms by the GCD
24 ÷ 12 = 2
36 ÷ 12 = 3
Simplified ratio = 2:3
Step 3: Express the result
24:36 = 2:3 (in simplest form)
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Verifying if 24:36 is equal to 2:3:
Method 1: Using fractions
24/36 = 24÷12/36÷12 = 2/3
2/3 = 2/3
Yes, they are equal ✓
Method 2: C...
Q3: If the ratio of two numbers is 3:5 and their sum is 40, find the numbers.
Given:
Ratio of two numbers = 3:5
Sum of the numbers = 40
Step 1: Represent the numbers using the ratio
Let the first number = 3x
Let the second number = 5x
(where x is a constant)
Step 2: Set up the equation using the sum
3x + 5x = 40
8x = 40
Step 3: Solve for x
x = 40 ÷ 8
x = 5
Step 4: Find the numbers
First number = 3x = 3 × 5 = 15
Second number = 5x = 5 × 5 = 25
Step 5: Verify
Ratio: 15:25 = 15÷5:25÷5 = 3:5 ✓
Sum: 15 + 25 = 40 ✓
Answer: The two numbers are 15 and 25.
Q4: What is a percentage? Convert 3/8 to percentage and 45% to a fraction.
Percentage:
A percentage is a ratio expressed as a fraction of 100.
The symbol '%' means "per hundred" or "out of 100".
Percentage is used to compare quantities easily.
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Converting 3/8 to Percentage:
Step 1: Convert the fraction to decimal
3/8 = 3 ÷ 8 = 0.375
Step 2: Multiply by 100 to get percentage
0.375 × 100 = 37.5%
Alternative method:
3/8 = 3/8 × 100% = (3 × 100)/8 % = 300/8 % = 37.5%
Answer: 3/8 = 37.5%
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Converting 45% to a Fraction:
Step 1: Write percent...
Q5: If a shirt costs Rs. 800 and a discount of 25% is given, what is the selling price?
Given:
Cost Price (CP) = Rs. 800
Discount = 25%
Step 1: Calculate the discount amount
Discount = 25% of 800
Discount = (25/100) × 800
Discount = 0.25 × 800
Discount = Rs. 200
Step 2: Calculate the Selling Price (SP)
Selling Price = Cost Price - Discount
SP = 800 - 200
SP = Rs. 600
Alternative method (Direct formula):
SP = CP × (100 - Discount%)/100
SP = 800 × (100 - 25)/100
SP = 800 × 75/100
SP = 800 × 0.75
SP = Rs. 600
Step 3: Verify
Discount given = Rs. 200
Selling Price = Rs. 600
Total = ...
Q6: What is simple interest? Calculate simple interest on Rs. 5000 at 8% per annum for 3 years.
Simple Interest (SI):
Simple interest is the interest calculated only on the principal amount.
Formula: SI = (P × R × T)/100
Where:
P = Principal (initial amount)
R = Rate of interest per annum (%)
T = Time period (in years)
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Given:
Principal (P) = Rs. 5000
Rate (R) = 8% per annum
Time (T) = 3 years
Step 1: Apply the simple interest formula
SI = (P × R × T)/100
SI = (5000 × 8 × 3)/100
Step 2: Calculate the numerator
5000 × 8 × 3 = 120,000
Step 3: Divide by 100
SI = 120,000/100
SI = Rs. 1...
Showing 6 of 8 questions. Visit the full page for complete solutions.
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