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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let's solve these questions step-by-step. Question 9: A person crossed a 600 meters long street in 4 minutes. What was his speed per hour? Step 1: Convert the distance to kilometers and time to hours. Distance = 600 meters = (600)/(1000) km = 0.6 km Time = 4 minutes = (4)/(60) hours = (1)/(15) hours Step 2: Calculate the speed. Speed = DistanceTime Speed = 0.6 km(1)/(15) hr = 0.6 × 15 km/hr 0.6 × 15 = 9 km/hr The correct option is (D). Answer: D) 9 km/hr <br> Question 10: In a company, a regular work time is 40 hours per week and the rate of payment for over time work is 1(1)/(2) times the regular rate (per hour). How much is the payment for an employee who worked 52 hours in a week if his hourly regular payment rate is 30? Step 1: Determine regular and overtime hours. Regular hours = 40 hours Total hours worked = 52 hours Overtime hours = Total hours worked - Regular hours 52 - 40 = 12 hours Step 2: Calculate regular and overtime payment rates. Regular rate = 30 birr/hour Overtime rate = 1(1)/(2) × Regular rate = 1.5 × 30 birr/hour 1.5 × 30 = 45 birr/hour Step 3: Calculate the total payment. Payment for regular hours = Regular hours × Regular rate 40 × 30 = 1200 birr Payment for overtime hours = Overtime hours × Overtime rate 12 × 45 = 540 birr Total payment = Payment for regular hours + Payment for overtime hours 1200 + 540 = 1740 birr The correct option is (C). Answer: C) Birr 1740 <br> Question 11: 20 friends went to a movie theatre. The average cost of the movie ticket for 19 friends was 120 birr. But one of the friends paid 38 birr more than the average cost for all the 19 friends. What was the total amount paid by all of them together? Step 1: Calculate the total cost for the 19 friends. Average cost for 19 friends = 120 birr Total cost for 19 friends = 19 × 120 birr 19 × 120 = 2280 birr Step 2: Calculate the cost for the 20th friend. The 20th friend paid 38 birr more than the average cost for the 19 friends. Cost for the 20th friend = 120 + 38 birr 120 + 38 = 158 birr Step 3: Calculate the total amount paid by all 20 friends. Total amount = Total cost for 19 friends + Cost for the 20th friend 2280 + 158 = 2438 birr The correct option is (A). Answer: A) 2,438 <br> Question 12: A retailer purchases shirts from a distributor at the rate of birr 300 per shirt and puts the label of birr 450 on each shirt. If the retailer allows some discount and still makes a profit of 23%, then what is the discount percentage offered by the shopkeeper? Step 1: Calculate the selling price (SP) of the shirt. Cost Price (CP) = 300 birr Profit percentage = 23% Selling Price (SP) = CP × (1 + Profit percentage) SP = 300 × (1 + 0.23) = 300 × 1.23 300 × 1.23 = 369 birr Step 2: Calculate the discount amount. Marked Price (MP) = 450 birr Discount = Marked Price - Selling Price 450 - 369 = 81 birr Step 3: Calculate the discount percentage. Discount percentage = DiscountMarked Price × 100\% (81)/(450) × 100\% = 0.18 × 100\% = 18\% The correct option is (C). Answer: C) 18% <br> Question 13: The speeds of two trains are in the ratio 6:7. If the second train runs 364 km in 4 hours, then the speed of the first train is _____. Step 1: Calculate the speed of the second train. Distance = 364 km Time = 4 hours Speed of second train = DistanceTime Speed of second train = 364 km4 hr = 91 km/hr Step 2: Use the given ratio to find the speed of the first train. Let the speeds of the first and second trains be S_1 and S_2 respectively. The ratio S_1 : S_2 = 6 : 7. So, (S_1)/(S_2) = (6)/(7). We know S_2 = 91 km/hr. (S_1)/(91) = (6)/(7) S_1 = (6)/(7) × 91 S_1 = 6 × 13 = 78 km/hr The correct option is (C). Answer: C) 78 km/hr <br> Question 14: Average of five numbers is 20. If each number is multiplied by 2, what will be the new average? Step 1: Understand the property of averages. If each number in a set is multiplied by a constant, the new average of the set will be the original average multiplied by that same constant. Step 2: Calculate the new average. Original average = 20 Each number is multiplied by 2. New average = Original average × 2 20 × 2 = 40 Alternatively: Sum of five numbers = Average × Number of numbers = 20 × 5 = 100. If each number is multiplied by 2, the new sum will be 100 × 2 = 200. New average = New sumNumber of numbers = (200)/(5) = 40. The correct option is (D). Answer: D) 40 All done for today! What's next?