{"title": "Word Problems on Quadratic Equations (Algebra) - Grade 10 ICSE - Part 2", "total_questions": 60, "questions": [{"id": 26, "difficulty": "medium", "question": "A man buys apples at ₹10 per dozen and same number at ₹15 per score. He mixes and sells at ₹20 per score, gaining ₹50. How many apples? 🍎", "options": {"A": "1200 apples", "B": "1000 apples", "C": "800 apples", "D": "600 apples"}, "correct_answer": "A"}, {"id": 27, "difficulty": "medium", "question": "The sum of ages of a man and his wife is 8 times sum of ages of their children. 2 years ago, sum was 10 times sum of children's ages then. 6 years later, sum will be 3 times sum of children's ages then. How many children? 👨‍👩‍👧‍👦", "options": {"A": "5 children", "B": "4 children", "C": "3 children", "D": "2 children"}, "correct_answer": "A"}, {"id": 28, "difficulty": "medium", "question": "A rectangular garden 50 m long and 34 m wide has path of uniform width around it. If area of path is 540 m², find width of path. 🌳", "options": {"A": "3 m", "B": "4 m", "C": "5 m", "D": "2.5 m"}, "correct_answer": "A"}, {"id": 29, "difficulty": "medium", "question": "A fast train takes 3 hours less than slow train for 600 km. If speed of slow train is 10 km/h less than fast, find speeds. 🚄", "options": {"A": "Fast=50 km/h, Slow=40 km/h", "B": "Fast=60 km/h, Slow=50 km/h", "C": "Fast=40 km/h, Slow=30 km/h", "D": "Fast=70 km/h, Slow=60 km/h"}, "correct_answer": "A"}, {"id": 30, "difficulty": "medium", "question": "If numerator and denominator of a fraction are increased by 1, fraction becomes 3/4. If decreased by 1, becomes 2/3. Find fraction. 🔢", "options": {"A": "5/7", "B": "4/5", "C": "3/4", "D": "2/3"}, "correct_answer": "A"}, {"id": 31, "difficulty": "medium", "question": "A plane left 30 minutes late. To reach destination 1500 km away on time, speed increased by 250 km/h. Find usual speed. ✈️", "options": {"A": "750 km/h", "B": "800 km/h", "C": "700 km/h", "D": "650 km/h"}, "correct_answer": "A"}, {"id": 32, "difficulty": "medium", "question": "The perimeter of a right triangle is 60 cm. Its hypotenuse is 25 cm. Find area. 📐", "options": {"A": "150 cm²", "B": "120 cm²", "C": "180 cm²", "D": "100 cm²"}, "correct_answer": "A"}, {"id": 33, "difficulty": "medium", "question": "A rectangular plot's length is twice breadth. If area is 288 m², find cost of fencing at ₹5 per meter. 🏡", "options": {"A": "₹720", "B": "₹600", "C": "₹840", "D": "₹960"}, "correct_answer": "A"}, {"id": 34, "difficulty": "medium", "question": "Sum of squares of three consecutive even numbers is 200. Find numbers. 🔢", "options": {"A": "6,8,10", "B": "4,6,8", "C": "8,10,12", "D": "2,4,6"}, "correct_answer": "A"}, {"id": 35, "difficulty": "medium", "question": "A student scored 150 marks in test but missed distinction by 10 marks. Had he scored 10% more, would have got distinction. Find max marks. 📝", "options": {"A": "200", "B": "250", "C": "300", "D": "350"}, "correct_answer": "A"}, {"id": 36, "difficulty": "medium", "question": "The product of two consecutive multiples of 5 is 300. Find them. ➗", "options": {"A": "15 and 20", "B": "10 and 15", "C": "20 and 25", "D": "25 and 30"}, "correct_answer": "A"}, {"id": 37, "difficulty": "medium", "question": "A two-digit number is 4 times sum of digits and twice product of digits. Find number. 🎯", "options": {"A": "36", "B": "24", "C": "48", "D": "12"}, "correct_answer": "A"}, {"id": 38, "difficulty": "medium", "question": "A train covers 300 km at uniform speed. If speed was 5 km/h more, would take 2 hours less. Find original time. ⏰", "options": {"A": "10 hours", "B": "12 hours", "C": "8 hours", "D": "15 hours"}, "correct_answer": "A"}, {"id": 39, "difficulty": "medium", "question": "The sum of squares of two numbers is 233 and one number is 3 less than twice the other. Find numbers. 🔥", "options": {"A": "8 and 13", "B": "7 and 11", "C": "5 and 7", "D": "12 and 15"}, "correct_answer": "A"}, {"id": 40, "difficulty": "medium", "question": "A rectangular metal sheet is 5 cm longer than wide. Equal squares of side 2 cm cut from corners, sheet folded to make open box of volume 150 cm³. Find dimensions. 📦", "options": {"A": "15 cm × 10 cm", "B": "20 cm × 15 cm", "C": "25 cm × 20 cm", "D": "18 cm × 13 cm"}, "correct_answer": "A"}, {"id": 41, "difficulty": "hard", "question": "A swimming pool is filled by two pipes. First pipe alone takes 5 hours more than second to fill. Together they fill in 6 hours. Find time each takes alone. 🏊", "options": {"A": "10 hours and 15 hours", "B": "15 hours and 10 hours", "C": "12 hours and 7 hours", "D": "9 hours and 4 hours"}, "correct_answer": "B"}, {"id": 42, "difficulty": "hard", "question": "A man bought oranges at ₹5 per dozen and same number at ₹4 per score. Sold at ₹6 per score, gaining ₹16. How many oranges? 🍊", "options": {"A": "960 oranges", "B": "720 oranges", "C": "840 oranges", "D": "600 oranges"}, "correct_answer": "A"}, {"id": 43, "difficulty": "hard", "question": "The area of a right triangle is 600 cm². If the hypotenuse is 50 cm, find perimeter. 📏", "options": {"A": "120 cm", "B": "100 cm", "C": "140 cm", "D": "160 cm"}, "correct_answer": "A"}, {"id": 44, "difficulty": "hard", "question": "A two-digit number is such that product of digits is 24. When 45 is added, digits interchange. Find number. 🔄", "options": {"A": "38", "B": "83", "C": "46", "D": "64"}, "correct_answer": "A"}, {"id": 45, "difficulty": "hard", "question": "A rectangular field's length is 20 m more than width. If cost of fencing is ₹3300 at ₹30 per meter, find area. 🌾", "options": {"A": "3500 m²", "B": "3000 m²", "C": "4000 m²", "D": "2500 m²"}, "correct_answer": "A"}, {"id": 46, "difficulty": "hard", "question": "The sum of squares of two consecutive odd numbers is 130. Find numbers. 🔢", "options": {"A": "7 and 9", "B": "5 and 7", "C": "9 and 11", "D": "3 and 5"}, "correct_answer": "A"}, {"id": 47, "difficulty": "hard", "question": "A train after traveling 150 km meets with accident, speed reduced to 4/5 of original, arrives 45 min late. If accident occurred 30 km later, would be 30 min late. Find original speed. 🚂", "options": {"A": "60 km/h", "B": "50 km/h", "C": "40 km/h", "D": "30 km/h"}, "correct_answer": "A"}, {"id": 48, "difficulty": "hard", "question": "The hypotenuse of a right triangle is 3√10 cm. If the smaller side is tripled and larger doubled, new hypotenuse is 9√5 cm. Find sides. 📐", "options": {"A": "3 cm and 9 cm", "B": "6 cm and 12 cm", "C": "9 cm and 12 cm", "D": "5 cm and 10 cm"}, "correct_answer": "A"}, {"id": 49, "difficulty": "hard", "question": "A rectangular plot's area is 528 m². Length is 1 more than twice breadth. Find cost of leveling at ₹2.50 per m². 🏞️", "options": {"A": "₹1320", "B": "₹1200", "C": "₹1500", "D": "₹1100"}, "correct_answer": "A"}, {"id": 50, "difficulty": "hard", "question": "Sum of squares of three consecutive multiples of 7 is 1225. Find them. 🔢", "options": {"A": "14,21,28", "B": "7,14,21", "C": "21,28,35", "D": "28,35,42"}, "correct_answer": "A"}, {"id": 51, "difficulty": "hard", "question": "A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours, goes 40 km upstream and 55 km downstream. Find speed in still water and stream. 🚤", "options": {"A": "Boat=8 km/h, Stream=3 km/h", "B": "Boat=10 km/h, Stream=4 km/h", "C": "Boat=12 km/h, Stream=6 km/h", "D": "Boat=6 km/h, Stream=2 km/h"}, "correct_answer": "A"}, {"id": 52, "difficulty": "hard", "question": "The sum of ages of father and son is 8 times sum of ages of sons. 4 years ago, sum was 10 times sum of sons' ages then. 8 years later, sum will be 3 times sum of sons' ages then. How many sons? 👨‍👦", "options": {"A": "5 sons", "B": "4 sons", "C": "3 sons", "D": "2 sons"}, "correct_answer": "A"}, {"id": 53, "difficulty": "hard", "question": "A rectangular sheet of metal is 2 cm longer than wide. Equal squares of side 3 cm cut from corners, folded to make open box of volume 765 cm³. Find dimensions. 📦", "options": {"A": "23 cm × 21 cm", "B": "25 cm × 23 cm", "C": "27 cm × 25 cm", "D": "29 cm × 27 cm"}, "correct_answer": "A"}, {"id": 54, "difficulty": "hard", "question": "The sum of squares of two numbers is 468 and difference is 18. Find numbers. 🔥", "options": {"A": "18 and 12", "B": "15 and 9", "C": "21 and 15", "D": "24 and 18"}, "correct_answer": "A"}, {"id": 55, "difficulty": "hard", "question": "A plane left 40 minutes late. To reach destination 1600 km away on time, speed increased by 400 km/h. Find usual speed. ✈️", "options": {"A": "800 km/h", "B": "900 km/h", "C": "700 km/h", "D": "600 km/h"}, "correct_answer": "A"}, {"id": 56, "difficulty": "hard", "question": "The perimeter of a right triangle is 70 cm. Its hypotenuse is 29 cm. Find area. 📐", "options": {"A": "210 cm²", "B": "180 cm²", "C": "240 cm²", "D": "150 cm²"}, "correct_answer": "A"}, {"id": 57, "difficulty": "hard", "question": "A two-digit number is 7 times sum of digits and also equal to 4 times product of digits. Find number. 🎯", "options": {"A": "84", "B": "42", "C": "21", "D": "63"}, "correct_answer": "A"}, {"id": 58, "difficulty": "hard", "question": "A train covers 400 km at uniform speed. If speed was 10 km/h more, would take 2 hours less. Find original time. ⏰", "options": {"A": "10 hours", "B": "8 hours", "C": "12 hours", "D": "15 hours"}, "correct_answer": "A"}, {"id": 59, "difficulty": "hard", "question": "The sum of squares of three consecutive odd numbers is 515. Find numbers. 🔢", "options": {"A": "11,13,15", "B": "9,11,13", "C": "13,15,17", "D": "7,9,11"}, "correct_answer": "A"}, {"id": 60, "difficulty": "hard", "question": "A rectangular plot's length is 3 times breadth. If area is 1200 m², find cost of fencing at ₹4 per meter. 🏡", "options": {"A": "₹640", "B": "₹720", "C": "₹800", "D": "₹560"}, "correct_answer": "A"}]}