StudentAayush Nayak
Class6-B
GradeGrade 6
SchoolYBIS
1.
Word Problem
(10 pts)
If Indian independence day is celebrated on 15th August, calculate the total number of days from 1st January of a leap year to 15th August. Show your working.
✎ Worked Solution
Step 1: Number of days in January = 31
Step 2: Number of days in February (leap year) = 29
Step 3: Number of days in March = 31
Step 4: Number of days in April = 30
Step 5: Number of days in May = 31
Step 6: Number of days in June = 30
Step 7: Number of days in July = 31
Step 8: Number of days until 15th August = 15
Total = 31 + 29 + 31 + 30 + 31 + 30 + 31 + 15
Answer: 228 days
2.
Word Problem
(10 pts)
A factory produces 125 widgets per day. Due to increased demand, they decide to work an extra day each fortnight. Calculate the increase in production after 3 months. Show your working.
✎ Worked Solution
Step 1: Number of days in 3 months assuming average 30 days per month = 90
Step 2: Number of extra days worked in 3 months (90 / 14 = 6 fortnights) = 6
Step 3: Total normal production in 3 months = 125 × 90
Step 4: Additional production = 125 × 6
Total increase in production = 125 × 6
Answer: 750 additional widgets
3.
Word Problem
(10 pts)
Swathi gets paid ₹ 45 per hour. She worked 35 hours one week, and 42 hours the next week. Calculate her total earnings for these two weeks. Show your working.
✎ Worked Solution
Step 1: Earnings for first week = 45 × 35
Step 2: Earnings for second week = 45 × 42
Total earnings = (45 × 35) + (45 × 42)
Answer: ₹ 3,465
4.
Word Problem
(10 pts)
A bookstore had a stock of 5,000 books. They sold 245 books each week for 4 weeks and then received a new shipment of 1,500. Calculate the current inventory. Show your working.
✎ Worked Solution
Step 1: Books sold in 4 weeks = 245 × 4
Step 2: Total stock after sales = 5,000 - (245 × 4)
Step 3: Current inventory after new shipment = (5,000 - 980) + 1,500
Answer: 5,520 books
5.
Word Problem
(10 pts)
A rectangular garden has a length that is twice its width. If the perimeter of the garden is 300 meters, find the dimensions of the garden. Show your working.
✎ Worked Solution
Step 1: Let width = W, then length = 2W
Step 2: Formula for perimeter = 2(length + width) = 2(2W + W)
Step 3: 6W = 300
Step 4: W = 300 / 6
Width = 50 meters, Length = 100 meters
Answer: Dimensions are 50 meters by 100 meters
6.
Word Problem
(10 pts)
A school fundraiser sells entry tickets at ₹ 150 each and raffle tickets at ₹ 25 each. If 240 entry tickets and 150 raffle tickets are sold, calculate the total revenue generated. Show your working.
✎ Worked Solution
Step 1: Revenue from entry tickets = 150 × 240
Step 2: Revenue from raffle tickets = 25 × 150
Total revenue = (150 × 240) + (25 × 150)
Answer: ₹ 39,750
7.
Word Problem
(10 pts)
A car travels at a constant speed of 90 km/h. Calculate the distance traveled in 3 hours and 45 minutes. Show your working.
✎ Worked Solution
Step 1: Convert 45 minutes to hours = 45/60 = 0.75
Step 2: Total time in hours = 3 + 0.75 = 3.75
Step 3: Distance = Speed × Time
Distance = 90 × 3.75
Answer: 337.5 km
8.
Word Problem
(10 pts)
A tank can be filled by a pipe in 4 hours and emptied by another pipe in 6 hours. If both pipes are opened together, how long will it take to fill the tank? Show your working.
✎ Worked Solution
Step 1: Rate of filling = 1/4 tank per hour
Step 2: Rate of emptying = 1/6 tank per hour
Step 3: Net rate = (1/4 - 1/6) tank per hour
Step 4: Net rate = 1/12 tank per hour
Time to fill = 1 / (1/12)
Answer: 12 hours
9.
Word Problem
(10 pts)
A grocer purchased a sack of rice weighing 60 kg. If he sells parts of it weighing 12.5 kg, 15 kg, and 23 kg, how much rice is left? Show your working.
✎ Worked Solution
Step 1: Total weight of rice sold = 12.5 + 15 + 23
Step 2: Total weight of rice sold = 50.5 kg
Step 3: Rice left = 60 - 50.5
Answer: 9.5 kg
10.
Word Problem
(10 pts)
An organization has a budget of ₹ 2,00,000 for projects. If it spends ₹ 52,750 on Project A, ₹ 68,945 on Project B, and ₹ 23,250 on Project C, how much budget remains? Show your working.
✎ Worked Solution
Step 1: Total expenditure = 52,750 + 68,945 + 23,250
Step 2: Total expenditure = 1,44,945
Step 3: Remaining budget = 2,00,000 - 1,44,945
Answer: ₹ 55,055