This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Here are the solutions to the word problems: 1. Sameer has 465 toffees that he wants to distribute on his birthday. He distributes 1/5 of these in the class. Out of the remaining toffees, he distributes 2/3 to his teachers. What is the number of toffees remaining with him? Step 1: Calculate toffees distributed to the class. Toffees to class = (1)/(5) × 465 = 93 Step 2: Calculate remaining toffees after distributing to the class. Remaining toffees = 465 - 93 = 372 Step 3: Calculate toffees distributed to teachers from the remaining. Toffees to teachers = (2)/(3) × 372 = 2 × 124 = 248 Step 4: Calculate the final number of toffees remaining with Sameer. Toffees remaining = 372 - 248 = 124 The number of toffees remaining with Sameer is 124 toffees. 2. A cup is 1/4 full of milk. What part of the cup is still to be filled by milk make it full? Step 1: Represent the full cup as 1. Step 2: Subtract the filled portion from the total to find the part to be filled. Part to be filled = 1 - (1)/(4) = (4)/(4) - (1)/(4) = (3)/(4) The part of the cup still to be filled is (3)/(4). 3. Ali divide 2 fruit cake equally among 6 persons. What part of the cake he gave to each persons? Step 1: Divide the total number of cakes by the number of persons. Part of cake per person = 2 cakes6 persons Step 2: Simplify the fraction. Part of cake per person = (2)/(6) = (1)/(3) Ali gave (1)/(3) of a cake to each person. 4. Rajesh purchased 2kg 500gms Potatoes, 300 gms of dhania, 6Kg 300gms Onion, 500gm palak & 2Kg 600gms tomatoes. Find the total weight of his Purchases in Kilograms? Step 1: Convert all weights to kilograms (1 kg = 1000 g). Potatoes = 2 kg 500 g = 2.5 kg Dhania = 300 g = 0.3 kg Onion = 6 kg 300 g = 6.3 kg Palak = 500 g = 0.5 kg Tomatoes = 2 kg 600 g = 2.6 kg Step 2: Sum all the weights. Total weight = 2.5 + 0.3 + 6.3 + 0.5 + 2.6 = 12.2 kg The total weight of his purchases is 12.2 kg. 5. A rectangle is divided into certain number of equal parts. If 20 of the parts so formed represent the fraction 1/5, find the number of parts in which the rectangle has been divided? Step 1: Let the total number of parts be x. Set up the proportion. (20)/(x) = (1)/(5) Step 2: Solve for x. x = 20 × 5 = 100 The rectangle has been divided into 100 parts. 6. The food we eat remains in the stomach for a maximum of 4 hours. For what fraction of a day, does it remain there? Step 1: Determine the total number of hours in a day. Hours in a day = 24 hours Step 2: Form a fraction of the time food remains in the stomach to the total hours in a day. Fraction = 4 hours24 hours Step 3: Simplify the fraction. Fraction = (1)/(6) The food remains in the stomach for (1)/(6) of a day. 7. Mr. Rakesh got a job at the age of 23 years & he got retired from the job at the age of 60 years. What fraction of his age till retirement was he in the job? Step 1: Calculate the duration Mr. Rakesh was in the job. Duration in job = 60 years - 23 years = 37 years Step 2: The age till retirement is 60 years. Form the fraction. Fraction = Duration in jobAge till retirement = (37)/(60) The fraction of his age till retirement that he was in the job is (37)/(60). 8. There are 12 dozen egg crates. 7/24 of them are rotten & 1/3 of them are to be sent back. How many crates can be used. Step 1: Calculate the total number of crates. (1 dozen = 12) Total crates = 12 dozen × 12 crates/dozen = 144 crates Step 2: Calculate the number of rotten crates. Rotten crates = (7)/(24) × 144 = 7 × 6 = 42 crates Step 3: Calculate the number of crates to be sent back. Crates to be sent back = (1)/(3) × 144 = 48 crates Step 4: Calculate the total number of unusable crates. Total unusable crates = 42 + 48 = 90 crates Step 5: Calculate the number of usable crates. Usable crates = 144 - 90 = 54 crates The number of crates that can be used is 54 crates. 9. Megha read 25 pages of a book containing 200 pages. Lalita read 2/5 of the same book. Who read less? Step 1: Determine the number of pages Megha read. Megha read = 25 pages Step 2: Calculate the number of pages Lalita read. Lalita read = (2)/(5) × 200 pages = 2 × 40 = 80 pages Step 3: Compare the number of pages read by Megha and Lalita. Since 25 pages (Megha) < 80 pages (Lalita), Megha read less. Megha read less. 10. Kabir exercised for 3/6 of an hour, while Rohit exercised for 3/4 of an hour. Who exercised for a longer time? Step 1: Simplify Kabir's exercise time. Kabir's time = (3)/(6) hour = (1)/(2) hour Step 2: Compare Kabir's time and Rohit's time. Kabir's time = (1)/(2) hour = (2)/(4) hour Rohit's time = (3)/(4) hour Since (3)/(4) > (2)/(4), Rohit exercised for a longer time. Rohit exercised for a longer time. Send me the next one 📸