I'll solve each problem step by step, checking my calculations carefully.
Q1: The weight of 12 sheets is 40 grams. How many sheets would weigh 1 kg?
First, let me convert 1 kg to grams: 1 kg = 1000 grams
If 12 sheets = 40 grams
Then 1 sheet = 40/12 = 10/3 grams
To find how many sheets make 1000 grams:
Number of sheets = 1000 ÷ (10/3) = 1000 × (3/10) = 300 sheets
Let me verify: 300 sheets × (10/3) grams per sheet = 300 × 10/3 = 1000 grams = 1 kg ✓
Answer for Q1:
300 (option 3)
---
Q2: A pump can fill a cistern in 2 hours. Due to a leak, it takes 2⅓ hours to fill it. How long does the leak take to empty the full tank?
Let's work with rates:
- Pump fills at rate: 1/2 tank per hour
- With leak, net filling rate: 1/(2⅓) = 1/(7/3) = 3/7 tank per hour
Let the leak's emptying rate be L tanks per hour.
Net rate = Pump rate - Leak rate
3/7 = 1/2 - L
L = 1/2 - 3/7
L = 7/14 - 6/14 = 1/14 tank per hour
So the leak empties 1/14 of the tank per hour.
Time to empty full tank = 1 ÷ (1/14) = 14 hours
Let me verify: If pump fills in 2 hours and leak empties in 14 hours:
Combined rate = 1/2 - 1/14 = 7/14 - 1/14 = 6/14 = 3/7 tank per hour
Time = 1 (3/7) = 7/3 = 2⅓ hours ✓
Answer for Q2:
14 hours (option 2)
---
Q3: 3 lambs finish eating turnips in 8 days. In how many days will 2 lambs finish them?
This is an inverse proportion problem. More lambs = fewer days, fewer lambs = more days.
Total work = 3 lambs × 8 days = 24 lamb-days
With 2 lambs:
Days needed = 24 lamb-days ÷ 2 lambs = 12 days
Let me verify: 2 lambs × 12 days = 24 lamb-days (same total work) ✓
Answer for Q3:
12 (option 4)
---
Q4: A does 20% less work than B. If A can finish a piece of work in 7½ hours, then B can finish it in:
If A does 20% less work than B, then:
A's efficiency = 80% of B's efficiency
A/B = 80/100 = 4/5
Since time is inversely proportional to efficiency:
Time_A / Time_B = Efficiency_B / Efficiency_A = 5/4
Given: Time_A = 7½ hours = 15/2 hours
(15/2) / Time_B = 5/4
Time_B = (15/2) × (4/5) = 60/10 = 6 hours
Let me verify: If B takes 6 hours and A takes 7.5 hours:
B's rate = 1/6 work per hour
A's rate = 1/7.5 = 2/15 work per hour
Ratio A:B = (2/15):(1/6) = (2/15)×6 = 12/15 = 4/5 = 80% ✓
Answer for Q4:
6 hours (option 3)
---
Q5: 14 workers can build a wall in 42 days. One worker can build it in:
This is an inverse proportion problem.
Total work = 14 workers × 42 days = 588 worker-days
With 1 worker:
Days needed = 588 worker-days ÷ 1 worker = 588 days
Let me verify: 1 worker × 588 days = 588 worker-days (same total work) ✓
Answer for Q5:
588 days (option 3)
──────────────────────────────────────
Final Answer:
Q1: 3 (300)
Q2: 2 (14 hours)
Q3: 4 (12)
Q4: 3 (6 hours)
Q5: 3 (588 days)
Parent Tip: Review the logic above to help your child master the concept of inverse proportion worksheet.
