{
  "title": "Word Problems (Quadratic Equations) - Grade 10 CBSE",
  "total_questions": 100,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "The product of two consecutive integers is 72. What is the smaller integer?", "options": {"A": "6", "B": "8", "C": "9", "D": "7"}, "correct_answer": "B"},
    {"id": 2, "difficulty": "easy", "question": "The area of a rectangle is 48 sq. units. If length is 4 more than width, find the width.", "options": {"A": "6", "B": "8", "C": "4", "D": "10"}, "correct_answer": "A"},
    {"id": 3, "difficulty": "easy", "question": "A number squared is 144. What is the positive number?", "options": {"A": "11", "B": "13", "C": "12", "D": "14"}, "correct_answer": "C"},
    {"id": 4, "difficulty": "easy", "question": "The sum of a number and its reciprocal is 2.5. What is the number?", "options": {"A": "2", "B": "0.5", "C": "3", "D": "4"}, "correct_answer": "A"},
    {"id": 5, "difficulty": "easy", "question": "A right triangle has hypotenuse 10 cm and one leg 6 cm. Find the other leg.", "options": {"A": "7", "B": "8", "C": "9", "D": "5"}, "correct_answer": "B"},
    {"id": 6, "difficulty": "easy", "question": "If (x+2)(x-3)=0, what is the positive solution?", "options": {"A": "2", "B": "3", "C": "-2", "D": "-3"}, "correct_answer": "B"},
    {"id": 7, "difficulty": "easy", "question": "The product of two numbers is 20 and their sum is 9. Find the smaller number.", "options": {"A": "4", "B": "5", "C": "6", "D": "7"}, "correct_answer": "A"},
    {"id": 8, "difficulty": "easy", "question": "A square has area 81 sq. units. What is its perimeter?", "options": {"A": "36", "B": "27", "C": "32", "D": "40"}, "correct_answer": "A"},
    {"id": 9, "difficulty": "easy", "question": "The sum of two numbers is 10 and their product is 24. Find the numbers (give the smaller).", "options": {"A": "3", "B": "4", "C": "5", "D": "6"}, "correct_answer": "B"},
    {"id": 10, "difficulty": "easy", "question": "If a number is added to its square, the result is 30. What is the number?", "options": {"A": "5", "B": "6", "C": "4", "D": "7"}, "correct_answer": "A"},
    {"id": 11, "difficulty": "easy", "question": "The length of a rectangle is 3 times its width. If area is 48, find width.", "options": {"A": "3", "B": "4", "C": "5", "D": "6"}, "correct_answer": "B"},
    {"id": 12, "difficulty": "easy", "question": "A train covers 300 km. If speed increased by 5 km/h, time reduces by 1 hour. Find original speed (in km/h).", "options": {"A": "20", "B": "25", "C": "30", "D": "35"}, "correct_answer": "B"},
    {"id": 13, "difficulty": "easy", "question": "The sum of squares of two consecutive even numbers is 100. Find the smaller.", "options": {"A": "4", "B": "6", "C": "8", "D": "10"}, "correct_answer": "B"},
    {"id": 14, "difficulty": "easy", "question": "If 3 times a number equals its square, find the non-zero number.", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "C"},
    {"id": 15, "difficulty": "easy", "question": "A natural number squared minus the number equals 20. Find the number.", "options": {"A": "4", "B": "5", "C": "6", "D": "7"}, "correct_answer": "B"},
    {"id": 16, "difficulty": "easy", "question": "The hypotenuse of right triangle is 13 cm, one side is 5 cm. Find other side.", "options": {"A": "10", "B": "11", "C": "12", "D": "13"}, "correct_answer": "C"},
    {"id": 17, "difficulty": "easy", "question": "Age of father is square of son's age. If sum is 42, find son's age.", "options": {"A": "5", "B": "6", "C": "7", "D": "8"}, "correct_answer": "B"},
    {"id": 18, "difficulty": "easy", "question": "If 2x² - 8 = 0, find positive solution.", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "B"},
    {"id": 19, "difficulty": "easy", "question": "Product of two consecutive odd numbers is 63. Find smaller.", "options": {"A": "5", "B": "7", "C": "9", "D": "11"}, "correct_answer": "B"},
    {"id": 20, "difficulty": "easy", "question": "If (x-4)(x+5)=0, what is positive solution?", "options": {"A": "4", "B": "5", "C": "-4", "D": "-5"}, "correct_answer": "A"},
    
    {"id": 21, "difficulty": "medium", "question": "Two squares have total area 41 sq. units. Side of one is 1 unit more than other. Find side of smaller square.", "options": {"A": "3", "B": "4", "C": "5", "D": "6"}, "correct_answer": "B"},
    {"id": 22, "difficulty": "medium", "question": "A train travels 150 km at uniform speed. If speed increased by 10 km/h, time reduces by 30 minutes. Find original speed.", "options": {"A": "40", "B": "50", "C": "60", "D": "70"}, "correct_answer": "B"},
    {"id": 23, "difficulty": "medium", "question": "The sum of a number and its reciprocal is 2.9. Find the number.", "options": {"A": "2", "B": "2.5", "C": "0.4", "D": "0.5"}, "correct_answer": "C"},
    {"id": 24, "difficulty": "medium", "question": "Perimeter of rectangle is 34 cm, area is 60 sq.cm. Find length.", "options": {"A": "10", "B": "11", "C": "12", "D": "13"}, "correct_answer": "C"},
    {"id": 25, "difficulty": "medium", "question": "Product of two numbers is 48, difference is 8. Find larger number.", "options": {"A": "10", "B": "11", "C": "12", "D": "13"}, "correct_answer": "C"},
    {"id": 26, "difficulty": "medium", "question": "A man is 5 times as old as his son. In 5 years, he'll be 3 times as old. Find current age of son.", "options": {"A": "5", "B": "6", "C": "7", "D": "8"}, "correct_answer": "A"},
    {"id": 27, "difficulty": "medium", "question": "If numerator increased by 2 and denominator by 1, fraction becomes 1. If numerator decreased by 1, fraction becomes 1/2. Find original fraction.", "options": {"A": "3/5", "B": "4/7", "C": "5/8", "D": "6/11"}, "correct_answer": "B"},
    {"id": 28, "difficulty": "medium", "question": "Sum of squares of three consecutive integers is 110. Find smallest integer.", "options": {"A": "5", "B": "6", "C": "7", "D": "8"}, "correct_answer": "A"},
    {"id": 29, "difficulty": "medium", "question": "A piece of cloth costs ₹200. If piece was 2m longer and each meter cost ₹1 less, cost would remain same. Find original length.", "options": {"A": "8", "B": "9", "C": "10", "D": "11"}, "correct_answer": "C"},
    {"id": 30, "difficulty": "medium", "question": "Two pipes fill tank in 12 hours. One takes 10 hours more than other alone. Find time for faster pipe alone.", "options": {"A": "15", "B": "20", "C": "25", "D": "30"}, "correct_answer": "B"},
    {"id": 31, "difficulty": "medium", "question": "Speed of boat in still water is 8 km/h. It goes 15 km upstream and returns in total 4 hours. Find speed of stream.", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "A"},
    {"id": 32, "difficulty": "medium", "question": "Find two numbers where sum is 27 and sum of squares is 369.", "options": {"A": "12,15", "B": "13,14", "C": "10,17", "D": "9,18"}, "correct_answer": "A"},
    {"id": 33, "difficulty": "medium", "question": "A right triangle has area 24 sq.cm. If hypotenuse is 10 cm, find perimeter.", "options": {"A": "20", "B": "22", "C": "24", "D": "26"}, "correct_answer": "C"},
    {"id": 34, "difficulty": "medium", "question": "Product of digits of two-digit number is 12. If 36 added to number, digits interchange. Find number.", "options": {"A": "26", "B": "34", "C": "43", "D": "62"}, "correct_answer": "A"},
    {"id": 35, "difficulty": "medium", "question": "Sum of ages of father and son is 50. 5 years ago, product was 175. Find current age of son.", "options": {"A": "10", "B": "12", "C": "14", "D": "15"}, "correct_answer": "D"},
    {"id": 36, "difficulty": "medium", "question": "A farmer has 60m fencing for rectangular plot. If length decreased by 3m and breadth increased by 1m, area unchanged. Find original length.", "options": {"A": "15", "B": "16", "C": "17", "D": "18"}, "correct_answer": "D"},
    {"id": 37, "difficulty": "medium", "question": "If 5 added to square of number, result is 9 times number. Find number.", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "D"},
    {"id": 38, "difficulty": "medium", "question": "Sum of reciprocals of two numbers is 7/10, product is 10. Find numbers (give larger).", "options": {"A": "4", "B": "5", "C": "6", "D": "7"}, "correct_answer": "B"},
    {"id": 39, "difficulty": "medium", "question": "A group of students planned picnic with budget ₹2400. 4 couldn't go, so each paid ₹10 more. Find original number of students.", "options": {"A": "20", "B": "22", "C": "24", "D": "26"}, "correct_answer": "C"},
    {"id": 40, "difficulty": "medium", "question": "Two consecutive natural numbers have product 342. Find sum of numbers.", "options": {"A": "35", "B": "36", "C": "37", "D": "38"}, "correct_answer": "C"},
    {"id": 41, "difficulty": "medium", "question": "Three consecutive integers have sum of squares 194. Find middle integer.", "options": {"A": "7", "B": "8", "C": "9", "D": "10"}, "correct_answer": "B"},
    {"id": 42, "difficulty": "medium", "question": "Time taken to cover 300 km reduced by 1 hour when speed increased by 10 km/h. Find original time.", "options": {"A": "5", "B": "6", "C": "7", "D": "8"}, "correct_answer": "B"},
    {"id": 43, "difficulty": "medium", "question": "If area of rectangle is 96 sq.units and diagonal is 14 units, find perimeter.", "options": {"A": "38", "B": "40", "C": "42", "D": "44"}, "correct_answer": "B"},
    {"id": 44, "difficulty": "medium", "question": "Sum of number and its square is 182. Find number.", "options": {"A": "12", "B": "13", "C": "14", "D": "15"}, "correct_answer": "B"},
    {"id": 45, "difficulty": "medium", "question": "Two numbers differ by 3 and their squares differ by 69. Find larger number.", "options": {"A": "10", "B": "11", "C": "12", "D": "13"}, "correct_answer": "C"},
    {"id": 46, "difficulty": "medium", "question": "A man bought oranges at ₹5 each. If price reduced by ₹1, he could buy 5 more oranges for ₹150. Find original number bought.", "options": {"A": "20", "B": "22", "C": "24", "D": "25"}, "correct_answer": "D"},
    {"id": 47, "difficulty": "medium", "question": "Hypotenuse of right triangle is 17 cm, difference of legs is 7 cm. Find area.", "options": {"A": "60", "B": "65", "C": "70", "D": "75"}, "correct_answer": "A"},
    {"id": 48, "difficulty": "medium", "question": "If 2 subtracted from number and result multiplied by 3, equals number squared. Find positive number.", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "C"},
    {"id": 49, "difficulty": "medium", "question": "Perimeter of rectangular field is 100m, area is 600 sq.m. Find difference between length and breadth.", "options": {"A": "8", "B": "10", "C": "12", "D": "14"}, "correct_answer": "B"},
    {"id": 50, "difficulty": "medium", "question": "One number is 5 more than another. Sum of squares is 97. Find smaller number.", "options": {"A": "4", "B": "5", "C": "6", "D": "7"}, "correct_answer": "A"},
    {"id": 51, "difficulty": "medium", "question": "A takes 2 hours more than B to walk 30 km. If A doubles speed, he takes 1 hour less than B. Find A's speed.", "options": {"A": "3", "B": "4", "C": "5", "D": "6"}, "correct_answer": "C"},
    {"id": 52, "difficulty": "medium", "question": "Sum of digits of two-digit number is 9. Number is 27 more than number with digits reversed. Find number.", "options": {"A": "36", "B": "45", "C": "54", "D": "63"}, "correct_answer": "D"},
    {"id": 53, "difficulty": "medium", "question": "Two taps fill tank in 3 hours 45 minutes. One fills in 4 hours less than other. Find time for faster tap alone.", "options": {"A": "5", "B": "6", "C": "7", "D": "8"}, "correct_answer": "B"},
    {"id": 54, "difficulty": "medium", "question": "If a number added to its square gives 42, what is the number?", "options": {"A": "5", "B": "6", "C": "7", "D": "8"}, "correct_answer": "B"},
    {"id": 55, "difficulty": "medium", "question": "Product of two numbers is 216. Sum of their squares is 468. Find sum of numbers.", "options": {"A": "28", "B": "30", "C": "32", "D": "34"}, "correct_answer": "B"},
    {"id": 56, "difficulty": "medium", "question": "A number is 2 more than its reciprocal. Find number.", "options": {"A": "1+√2", "B": "2+√3", "C": "2", "D": "3"}, "correct_answer": "A"},
    {"id": 57, "difficulty": "medium", "question": "Sum of squares of three consecutive even numbers is 200. Find smallest number.", "options": {"A": "6", "B": "8", "C": "10", "D": "12"}, "correct_answer": "B"},
    {"id": 58, "difficulty": "medium", "question": "If numerator increased by 1 and denominator decreased by 1, fraction becomes 1. If both increased by 1, fraction becomes 3/4. Find original fraction.", "options": {"A": "2/5", "B": "3/7", "C": "4/9", "D": "5/11"}, "correct_answer": "A"},
    {"id": 59, "difficulty": "medium", "question": "Three consecutive integers have sum of squares 149. Find sum of integers.", "options": {"A": "18", "B": "19", "C": "20", "D": "21"}, "correct_answer": "D"},
    {"id": 60, "difficulty": "medium", "question": "A rectangular plot length twice breadth. If length decreased by 5m and breadth increased by 5m, area increases by 75 sq.m. Find original area.", "options": {"A": "400", "B": "450", "C": "500", "D": "550"}, "correct_answer": "B"},
    {"id": 61, "difficulty": "medium", "question": "If sum of number and its square is 240, find number.", "options": {"A": "14", "B": "15", "C": "16", "D": "17"}, "correct_answer": "B"},
    {"id": 62, "difficulty": "medium", "question": "Speed of boat in still water is 15 km/h. It goes 30 km upstream and returns in 4.5 hours. Find speed of stream.", "options": {"A": "3", "B": "4", "C": "5", "D": "6"}, "correct_answer": "C"},
    {"id": 63, "difficulty": "medium", "question": "Two numbers differ by 4 and product is 96. Find sum of numbers.", "options": {"A": "18", "B": "20", "C": "22", "D": "24"}, "correct_answer": "B"},
    {"id": 64, "difficulty": "medium", "question": "A takes 6 hours more than B to cover 72 km. If A doubles speed, he takes 1 hour less than B. Find A's original speed.", "options": {"A": "4", "B": "5", "C": "6", "D": "7"}, "correct_answer": "A"},
    {"id": 65, "difficulty": "medium", "question": "Sum of squares of two numbers is 130, product is 63. Find sum of numbers.", "options": {"A": "14", "B": "15", "C": "16", "D": "17"}, "correct_answer": "C"},
    {"id": 66, "difficulty": "medium", "question": "If 1 added to product of two consecutive integers, result is 15 less than square of larger. Find smaller integer.", "options": {"A": "6", "B": "7", "C": "8", "D": "9"}, "correct_answer": "A"},
    {"id": 67, "difficulty": "medium", "question": "A pole of height 10m broke such that top touched ground 6m from base. Find height of break point.", "options": {"A": "4", "B": "4.5", "C": "5", "D": "5.5"}, "correct_answer": "C"},
    {"id": 68, "difficulty": "medium", "question": "Two-digit number exceeds sum of digits by 54. Digits differ by 2. Find number.", "options": {"A": "64", "B": "75", "C": "86", "D": "97"}, "correct_answer": "B"},
    {"id": 69, "difficulty": "medium", "question": "Sum of ages of father and son is 56. 4 years ago, father was 3 times as old. Find current age of son.", "options": {"A": "12", "B": "14", "C": "16", "D": "18"}, "correct_answer": "C"},
    {"id": 70, "difficulty": "medium", "question": "If area of right triangle is 30 sq.cm and hypotenuse 13 cm, find sum of legs.", "options": {"A": "15", "B": "16", "C": "17", "D": "18"}, "correct_answer": "C"},
    {"id": 71, "difficulty": "medium", "question": "A number squared exceeds the number by 72. Find number.", "options": {"A": "8", "B": "9", "C": "10", "D": "11"}, "correct_answer": "B"},
    {"id": 72, "difficulty": "medium", "question": "Three consecutive integers have product equal to sum of first and third. Find middle integer.", "options": {"A": "0", "B": "1", "C": "2", "D": "3"}, "correct_answer": "C"},
    {"id": 73, "difficulty": "medium", "question": "If 5 subtracted from number and result squared, equals 4 times number. Find positive number.", "options": {"A": "5", "B": "6", "C": "7", "D": "8"}, "correct_answer": "A"},
    {"id": 74, "difficulty": "medium", "question": "A rectangular park perimeter 80m, area 400 sq.m. Find length.", "options": {"A": "20", "B": "22", "C": "24", "D": "26"}, "correct_answer": "A"},
    {"id": 75, "difficulty": "medium", "question": "Sum of reciprocals of two numbers is 1/2, product is 20. Find numbers (give larger).", "options": {"A": "8", "B": "9", "C": "10", "D": "11"}, "correct_answer": "C"},
    {"id": 76, "difficulty": "medium", "question": "If 3 added to square of number equals 12 times number, find number.", "options": {"A": "0.5", "B": "0.25", "C": "0.3", "D": "0.4"}, "correct_answer": "C"},
    {"id": 77, "difficulty": "medium", "question": "Two numbers have sum 15 and sum of squares 113. Find product.", "options": {"A": "54", "B": "55", "C": "56", "D": "57"}, "correct_answer": "C"},
    {"id": 78, "difficulty": "medium", "question": "A takes 3 hours more than B to cover 30 km. If A doubles speed, he takes 1 hour less than B. Find B's speed.", "options": {"A": "4", "B": "5", "C": "6", "D": "7"}, "correct_answer": "B"},
    {"id": 79, "difficulty": "medium", "question": "If perimeter of rectangle is 28 cm and diagonal is 10 cm, find area.", "options": {"A": "46", "B": "47", "C": "48", "D": "49"}, "correct_answer": "C"},
    {"id": 80, "difficulty": "medium", "question": "Sum of number and twice its reciprocal is 3. Find number.", "options": {"A": "1", "B": "2", "C": "0.5", "D": "1.5"}, "correct_answer": "B"},
    
    {"id": 81, "difficulty": "hard", "question": "Solve: 1/(x-1) + 2/(x+1) = 2", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "D"},
    {"id": 82, "difficulty": "hard", "question": "Find k if equations x²-5x+k=0 and x²-8x+2k=0 have a common root.", "options": {"A": "0", "B": "4", "C": "8", "D": "12"}, "correct_answer": "B"},
    {"id": 83, "difficulty": "hard", "question": "If α,β are roots of 2x²+5x+1=0, find α²+β².", "options": {"A": "21/4", "B": "23/4", "C": "25/4", "D": "27/4"}, "correct_answer": "A"},
    {"id": 84, "difficulty": "hard", "question": "If difference of roots of x²-px+8=0 is 2, find p.", "options": {"A": "±4", "B": "±5", "C": "±6", "D": "±7"}, "correct_answer": "C"},
    {"id": 85, "difficulty": "hard", "question": "Find k so that x²+2x+k=0 has real and equal roots.", "options": {"A": "0", "B": "1", "C": "2", "D": "3"}, "correct_answer": "B"},
    {"id": 86, "difficulty": "hard", "question": "If sum of squares of roots of x²-3x+k=0 is 17, find k.", "options": {"A": "-4", "B": "-2", "C": "2", "D": "4"}, "correct_answer": "A"},
    {"id": 87, "difficulty": "hard", "question": "Solve: √(x+3) + √(x-2) = 5", "options": {"A": "3", "B": "4", "C": "5", "D": "6"}, "correct_answer": "D"},
    {"id": 88, "difficulty": "hard", "question": "Find k if one root of 3x²-8x+2k+1=0 is 3 times other.", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "C"},
    {"id": 89, "difficulty": "hard", "question": "If α,β are roots of 3x²-6x+4=0, find α³+β³.", "options": {"A": "0", "B": "2", "C": "4", "D": "6"}, "correct_answer": "A"},
    {"id": 90, "difficulty": "hard", "question": "Solve: (x²-3x)² - 8(x²-3x) + 12 = 0", "options": {"A": "1,2,3,4", "B": "1,2,4,5", "C": "1,3,4,5", "D": "2,3,4,5"}, "correct_answer": "B"},
    {"id": 91, "difficulty": "hard", "question": "If ratio of roots of 4x²-16x+λ=0 is 1:3, find λ.", "options": {"A": "10", "B": "11", "C": "12", "D": "13"}, "correct_answer": "C"},
    {"id": 92, "difficulty": "hard", "question": "Find condition that roots of ax²+2bx+c=0 are reciprocal of each other.", "options": {"A": "a=c", "B": "b²=ac", "C": "a+b=c", "D": "2b=a+c"}, "correct_answer": "A"},
    {"id": 93, "difficulty": "hard", "question": "If roots of x²+px+q=0 are in ratio 2:3 and sum of roots is 15, find product.", "options": {"A": "50", "B": "52", "C": "54", "D": "56"}, "correct_answer": "C"},
    {"id": 94, "difficulty": "hard", "question": "Solve: 2^(2x) - 10·2^x + 16 = 0", "options": {"A": "1,2", "B": "1,3", "C": "2,3", "D": "3,4"}, "correct_answer": "B"},
    {"id": 95, "difficulty": "hard", "question": "If α,β are roots of x²-2x+3=0, find equation with roots α+2, β+2.", "options": {"A": "x²-6x+11=0", "B": "x²-6x+9=0", "C": "x²-4x+7=0", "D": "x²-4x+5=0"}, "correct_answer": "A"},
    {"id": 96, "difficulty": "hard", "question": "Find k if sum of roots of 2x²-kx+8=0 equals product.", "options": {"A": "4", "B": "6", "C": "8", "D": "10"}, "correct_answer": "C"},
    {"id": 97, "difficulty": "hard", "question": "If one root of x²+ax+8=0 is square of other, find a.", "options": {"A": "-6", "B": "-4", "C": "4", "D": "6"}, "correct_answer": "A"},
    {"id": 98, "difficulty": "hard", "question": "Solve: |x-3|² - 4|x-3| + 3 = 0", "options": {"A": "0,2,4,6", "B": "1,2,4,5", "C": "2,3,4,5", "D": "1,3,4,6"}, "correct_answer": "A"},
    {"id": 99, "difficulty": "hard", "question": "If α,β are roots of 2x²-4x+1=0, find α/β + β/α.", "options": {"A": "2", "B": "4", "C": "6", "D": "8"}, "correct_answer": "C"},
    {"id": 100, "difficulty": "hard", "question": "Find k if equations x²+x+k=0 and x²+kx+1=0 have a common root.", "options": {"A": "-2", "B": "-1", "C": "1", "D": "2"}, "correct_answer": "A"}
  ]
}