Complete step-by-step solutions for DAV Class 7 Secondary Mathematics Chapter 5: Application of Percentage (Brain Teasers, HOTS & Value Based Questions). Covers all profit and loss computations, cost price, selling price, simple interest formulas, percentage comparisons, Higher Order Thinking Skills (HOTS), and Value-Based Questions (VBQs) strictly aligned with the DAV Education Board curriculum.
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Q.1. (A) Tick (✓) the correct option
(i) 12% of 50 + 5% of 120 is equal to:
- (a) 10
- (b) 15
- (c) 12
- (d) 20
• 12% of 50 = (12/100) × 50 = 6.
• 5% of 120 = (5/100) × 120 = 600/100 = 6.
Sum = 6 + 6 = 12.
Correct Option: (c) 12
(ii) What is 50% of a number whose 200% is 20?
- (a) 15
- (b) 5
- (c) 20
- (d) 10
Let the number be x.
200% of x = 20 ⇒ 2x = 20 ⇒ x = 10.
Now, 50% of 10 = (50/100) × 10 = 5.
Correct Option: (b) 5
(iii) At what rate of simple interest per annum will ₹2500 grow to ₹4000 in 5 years?
- (a) 10%
- (b) 15%
- (c) 12%
- (d) 13%
Principal P = ₹2500, Amount A = ₹4000 ⇒ Simple Interest SI = 4000 − 2500 = ₹1500.
Time T = 5 years.
R = (SI × 100)/(P × T) = (1500 × 100)/(2500 × 5) = 1500/125 = 12% p.a.
Correct Option: (c) 12%
(iv) Rohan gave a tip of ₹30 to a delivery person, which was 20% of his pizza order. How much did the pizza cost him?
- (a) ₹150
- (b) ₹180
- (c) ₹140
- (d) ₹200
Let pizza cost be ₹x.
20% of x = 30 ⇒ (20/100) × x = 30 ⇒ x = 30 × 5 = ₹150.
Correct Option: (a) ₹150
(v) If Cost Price = ₹80 and Selling Price = ₹100, the Gain% is:
- (a) 20%
- (b) 25%
- (c) 15%
- (d) 30%
Gain = SP − CP = 100 − 80 = ₹20.
Gain% = (Gain/CP) × 100 = (20/80) × 100 = 100/4 = 25%.
Correct Option: (b) 25%
Q.1. (B) Short Answer Questions
(a) Convert the fraction 3/8 into a percentage.
Ans: 37.5%
(b) What percentage of 2 km is 250 metres?
Percentage = (250/2000) × 100% = 25/2% = 12.5%.
Ans: 12.5%
(c) State whether profit or loss is always calculated on Cost Price or Selling Price.
Ans: Profit percentage and Loss percentage are always calculated on the Cost Price (CP) of the article.
(d) Write the formula to find the Cost Price when SP and Gain% are given.
Ans: CP = (SP × 100)/(100 + Gain%).
Q.2. Word Problems on Profit, Loss & Simple Interest
(i) By selling an electric fan for ₹660, a dealer gains 10%. Find the Cost Price of the fan.
CP = (SP × 100)/(100 + Gain%) = (660 × 100)/(100 + 10) = 66000/110 = ₹600.
Ans: ₹600
(ii) A sum of money triples itself in 10 years under simple interest. Find the rate of interest per annum.
Amount after 10 years A = 3P ⇒ Simple Interest SI = 3P − P = 2P.
Time T = 10 years.
SI = (P × R × T)/100
2P = (P × R × 10)/100
2 = R/10 ⇒ R = 20% p.a.
Ans: 20% per annum
🔥 Higher Order Thinking Skills (HOTS)
HOTS Q1: If the price of cooking oil rises by 25%, by what percentage must a family reduce its consumption so that its expenditure does not increase?
= 25/(100 + 25) × 100% = 25/125 × 100% = 1/5 × 100% = 20%.
Ans: 20%
HOTS Q2: A shopkeeper sold two table lamps for ₹1980 each. On one he made a profit of 10% and on the other he suffered a loss of 10%. Find his overall gain or loss percent.
• Second lamp CP = (1980 × 100)/90 = ₹2200.
Total CP = 1800 + 2200 = ₹4000.
Total SP = 1980 + 1980 = ₹3960.
Since Total CP > Total SP, there is a Net Loss = 4000 − 3960 = ₹40.
Net Loss% = (40/4000) × 100% = 1% Loss.
Ans: 1% Loss (Loss = ₹40)
🌱 Value Based Questions (VBQ)
VBQ: An employee earns an annual salary of ₹4,50,000. He deposits 5% of his income into a charitable trust that funds school books and nutrition for underprivileged children.
(a) How much money does the employee donate annually?
Donation = 5% of ₹4,50,000 = (5/100) × 4,50,000 = ₹22,500.(b) What moral quality does this charitable action demonstrate?
Core Values Depicted: Social empathy, philanthropy, generosity, civic contribution, and commitment to educational equality for disadvantaged youth.Ans: (a) ₹22,500 | (b) Generosity, Social Responsibility
📚 DAV Class 7 Maths Chapter 5: Application of Percentage – Complete Solutions Index
| Worksheet / Section | Topics Covered | Solution Link |
|---|---|---|
| Worksheet 1 | Conversions between Percentages, Fractions & Decimals | View Worksheet 1 → |
| Worksheet 2 | Percentage of Quantities & Percentage Increase/Decrease | View Worksheet 2 → |
| Worksheet 3 | Profit and Loss, Gain% & Loss% Calculations | View Worksheet 3 → |
| Worksheet 4 | Simple Interest (I = PRT/100, Principal & Rate) | View Worksheet 4 → |
| Worksheet 5 | Comprehensive Real-Life Financial Problems | View Worksheet 5 → |
| Brain Teasers, HOTS & VBQs | Consumption Shifts, Tripling Sums & Simultaneous Sales | Current Page |