{"title": "Word Problems (Simultaneous Linear Equations) - Grade 9 ICSE","total_questions": 60,"questions": [{"id": 1,"difficulty": "easy","question": "The sum of two numbers is 25 and their difference is 5. Find the numbers. 🔢","options": {"A": "10, 15","B": "12, 13","C": "15, 10","D": "20, 5"},"correct_answer": "C"},{"id": 2,"difficulty": "easy","question": "If 5 pens and 3 pencils cost ₹45, and 2 pens and 5 pencils cost ₹35, find cost of 1 pen. ✏️","options": {"A": "₹5","B": "₹6","C": "₹7","D": "₹8"},"correct_answer": "B"},{"id": 3,"difficulty": "easy","question": "A father is 30 years older than his son. In 5 years, his age will be twice the son's age. Find son's present age. 👨‍👦","options": {"A": "20","B": "25","C": "30","D": "35"},"correct_answer": "B"},{"id": 4,"difficulty": "easy","question": "The perimeter of a rectangle is 40 cm. Its length is 4 cm more than its breadth. Find length. 📏","options": {"A": "10 cm","B": "12 cm","C": "14 cm","D": "16 cm"},"correct_answer": "B"},{"id": 5,"difficulty": "easy","question": "Two numbers are in ratio 3:4. If 5 is added to each, ratio becomes 4:5. Find smaller number. 🔄","options": {"A": "10","B": "15","C": "20","D": "25"},"correct_answer": "B"},{"id": 6,"difficulty": "easy","question": "A total of ₹500 is in coins of ₹5 and ₹10. If there are 70 coins in total, how many ₹5 coins? 💰","options": {"A": "30","B": "40","C": "50","D": "60"},"correct_answer": "B"},{"id": 7,"difficulty": "easy","question": "The sum of digits of a two-digit number is 9. Reversing digits gives a number 45 less. Find original number. 🔢","options": {"A": "36","B": "45","C": "54","D": "72"},"correct_answer": "D"},{"id": 8,"difficulty": "easy","question": "In a class, if 2 students sit on each bench, 10 benches are empty. If 3 sit, 5 students are left. How many students? 🪑","options": {"A": "60","B": "70","C": "80","D": "90"},"correct_answer": "C"},{"id": 9,"difficulty": "easy","question": "A fraction becomes 2/3 if 1 is added to both numerator and denominator. If 1 is subtracted, it becomes 1/2. Find fraction. ➗","options": {"A": "3/5","B": "5/7","C": "7/9","D": "9/11"},"correct_answer": "A"},{"id": 10,"difficulty": "easy","question": "A boat goes 15 km upstream and 22 km downstream in 5 hours. Upstream speed = 3 km/h, downstream speed = 5 km/h. Find boat speed in still water. 🚤","options": {"A": "4 km/h","B": "5 km/h","C": "6 km/h","D": "7 km/h"},"correct_answer": "A"},{"id": 11,"difficulty": "easy","question": "The sum of ages of mother and daughter is 50. 5 years ago, mother was 7 times as old. Find daughter's age now. 👩‍👧","options": {"A": "8","B": "10","C": "12","D": "15"},"correct_answer": "B"},{"id": 12,"difficulty": "easy","question": "3 chairs and 2 tables cost ₹1800. 5 chairs and 3 tables cost ₹2900. Find cost of a table. 🪑","options": {"A": "₹400","B": "₹500","C": "₹600","D": "₹700"},"correct_answer": "C"},{"id": 13,"difficulty": "easy","question": "A two-digit number is 4 times sum of its digits. If 18 is added, digits reverse. Find number. 🔢","options": {"A": "24","B": "36","C": "48","D": "64"},"correct_answer": "A"},{"id": 14,"difficulty": "easy","question": "Hema bought 5 notebooks and 2 pens for ₹110. Rina bought 3 notebooks and 4 pens for ₹90. Find notebook cost. 📓","options": {"A": "₹15","B": "₹20","C": "₹25","D": "₹30"},"correct_answer": "B"},{"id": 15,"difficulty": "easy","question": "The difference between two numbers is 14 and their sum is 36. Find larger number. ➖","options": {"A": "20","B": "22","C": "24","D": "25"},"correct_answer": "D"},{"id": 16,"difficulty": "easy","question": "If 1 is added to numerator and denominator, fraction = 3/4. If 1 subtracted, fraction = 2/3. Find original. ➗","options": {"A": "5/7","B": "7/9","C": "9/11","D": "11/13"},"correct_answer": "A"},{"id": 17,"difficulty": "easy","question": "A train travels 300 km at uniform speed. If speed were 5 km/h more, time would be 2 hours less. Find original speed. 🚂","options": {"A": "20 km/h","B": "25 km/h","C": "30 km/h","D": "35 km/h"},"correct_answer": "B"},{"id": 18,"difficulty": "easy","question": "Sum of digits = 7. Difference between number and number with digits reversed = 27. Find number. 🔄","options": {"A": "25","B": "34","C": "43","D": "52"},"correct_answer": "D"},{"id": 19,"difficulty": "easy","question": "5 kg apples and 3 kg oranges cost ₹430. 2 kg apples and 6 kg oranges cost ₹470. Find apple price per kg. 🍎","options": {"A": "₹50","B": "₹60","C": "₹70","D": "₹80"},"correct_answer": "A"},{"id": 20,"difficulty": "easy","question": "A number consists of two digits. Digit at ten's place is twice unit's digit. If 27 is added, digits reverse. Find number. 🔢","options": {"A": "36","B": "48","C": "63","D": "84"},"correct_answer": "C"},{"id": 21,"difficulty": "medium","question": "A man has ₹10,000 in ₹200 and ₹500 notes. If total notes are 35, how many ₹500 notes? 💵","options": {"A": "10","B": "15","C": "20","D": "25"},"correct_answer": "A"},{"id": 22,"difficulty": "medium","question": "A fraction's denominator is 4 more than numerator. Adding 1 to both gives 2/3. Find fraction. ➗","options": {"A": "7/11","B": "9/13","C": "11/15","D": "13/17"},"correct_answer": "A"},{"id": 23,"difficulty": "medium","question": "A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours, it goes 40 km upstream and 55 km downstream. Find speed in still water. 🚤","options": {"A": "8 km/h","B": "10 km/h","C": "12 km/h","D": "14 km/h"},"correct_answer": "A"},{"id": 24,"difficulty": "medium","question": "Sum of ages of father and son is 45. 5 years ago, product of ages was 124. Find current ages. 👨‍👦","options": {"A": "30, 15","B": "32, 13","C": "35, 10","D": "36, 9"},"correct_answer": "D"},{"id": 25,"difficulty": "medium","question": "A two-digit number is 5 times sum of digits. If 9 is subtracted, digits reverse. Find number. 🔢","options": {"A": "45","B": "54","C": "63","D": "72"},"correct_answer": "A"},{"id": 26,"difficulty": "medium","question": "3 men and 2 women can do a work in 12 days; 2 men and 3 women in 13 days. Find days for 1 woman alone. 👩‍💼","options": {"A": "30","B": "35","C": "40","D": "45"},"correct_answer": "C"},{"id": 27,"difficulty": "medium","question": "If numerator increased by 2 and denominator by 1, fraction = 3/4. If both decreased by 1, fraction = 2/3. Find fraction. ➗","options": {"A": "7/11","B": "8/13","C": "9/14","D": "10/17"},"correct_answer": "A"},{"id": 28,"difficulty": "medium","question": "A train covers distance between two stations at uniform speed. If speed increased by 10 km/h, time reduces by 30 minutes. If speed reduced by 10 km/h, time increases by 45 minutes. Find distance. 🚂","options": {"A": "200 km","B": "250 km","C": "300 km","D": "350 km"},"correct_answer": "C"},{"id": 29,"difficulty": "medium","question": "The sum of digits of a two-digit number is 11. If 63 is added, digits reverse. Find number. 🔢","options": {"A": "29","B": "38","C": "47","D": "56"},"correct_answer": "A"},{"id": 30,"difficulty": "medium","question": "A man buys 5 horses and 7 cows for ₹5850. He sells horses at 10% profit, cows at 20% profit, earning ₹7110. Find cost of a horse. 🐴","options": {"A": "₹500","B": "₹600","C": "₹700","D": "₹800"},"correct_answer": "B"},{"id": 31,"difficulty": "medium","question": "The sum of two numbers is 52. Their LCM is 168 and HCF is 4. Find numbers. 🔢","options": {"A": "20,32","B": "24,28","C": "16,36","D": "12,40"},"correct_answer": "B"},{"id": 32,"difficulty": "medium","question": "A person invested ₹20,000 in two schemes at 8% and 10% interest. Total annual interest ₹1760. Find amount at 8%. 💰","options": {"A": "₹8000","B": "₹10,000","C": "₹12,000","D": "₹14,000"},"correct_answer": "C"},{"id": 33,"difficulty": "medium","question": "A number consists of two digits whose sum is 10. If 36 is added, digits reverse. Find number. 🔄","options": {"A": "37","B": "46","C": "55","D": "64"},"correct_answer": "A"},{"id": 34,"difficulty": "medium","question": "5 years ago, mother was 3 times as old as daughter. 10 years later, mother will be twice as old. Find daughter's age now. 👩‍👧","options": {"A": "15","B": "18","C": "20","D": "22"},"correct_answer": "C"},{"id": 35,"difficulty": "medium","question": "A man rowing upstream takes 6 hours for 24 km, downstream takes 4 hours for same distance. Find speed of stream. 🚣","options": {"A": "0.5 km/h","B": "1 km/h","C": "1.5 km/h","D": "2 km/h"},"correct_answer": "B"},{"id": 36,"difficulty": "medium","question": "The sum of a number and its reciprocal is 25/12. Find number. 🔄","options": {"A": "3/4","B": "4/3","C": "5/4","D": "4/5"},"correct_answer": "B"},{"id": 37,"difficulty": "medium","question": "A chemist has two solutions of acid: 50% and 25%. To get 10 liters of 40% acid, how much of each needed? 🧪","options": {"A": "6L, 4L","B": "5L, 5L","C": "7L, 3L","D": "8L, 2L"},"correct_answer": "A"},{"id": 38,"difficulty": "medium","question": "If 1 is added to numerator of fraction, it becomes 1. If 1 added to denominator, it becomes 1/2. Find fraction. ➗","options": {"A": "1/3","B": "2/5","C": "3/7","D": "4/9"},"correct_answer": "B"},{"id": 39,"difficulty": "medium","question": "A rectangle's length is 5 m more than breadth. If perimeter is 50 m, find area. 📐","options": {"A": "100 m²","B": "125 m²","C": "150 m²","D": "175 m²"},"correct_answer": "C"},{"id": 40,"difficulty": "medium","question": "Sum of ages of A and B is 45. 5 years ago, A was twice as old as B. Find A's age now. 👫","options": {"A": "25","B": "28","C": "30","D": "32"},"correct_answer": "C"},{"id": 41,"difficulty": "hard","question": "A train passes two persons walking at 3 km/h and 4.5 km/h in same direction in 9 sec and 10 sec respectively. Find train length. 🚂","options": {"A": "100 m","B": "125 m","C": "150 m","D": "175 m"},"correct_answer": "B"},{"id": 42,"difficulty": "hard","question": "The sum of digits of a two-digit number is 13. If digits interchange and number subtracted from original, result is 45. Find number. 🔢","options": {"A": "67","B": "76","C": "85","D": "94"},"correct_answer": "D"},{"id": 43,"difficulty": "hard","question": "A man invests ₹30,000 partly at 5% and rest at 8% interest. Total annual income ₹2100. How much at 5%? 💵","options": {"A": "₹10,000","B": "₹12,000","C": "₹15,000","D": "₹18,000"},"correct_answer": "A"},{"id": 44,"difficulty": "hard","question": "The ratio of incomes of A and B is 9:7 and expenditure ratio 4:3. If each saves ₹2000, find A's income. 💰","options": {"A": "₹16,000","B": "₹18,000","C": "₹20,000","D": "₹22,000"},"correct_answer": "B"},{"id": 45,"difficulty": "hard","question": "A number of two digits is such that product of digits is 18. If 27 is added, digits interchange. Find number. 🔢","options": {"A": "36","B": "63","C": "92","D": "29"},"correct_answer": "A"},{"id": 46,"difficulty": "hard","question": "A boat goes 20 km upstream and 30 km downstream in 8 hours. It goes 30 km upstream and 20 km downstream in 9.5 hours. Find stream speed. 🚣","options": {"A": "2 km/h","B": "2.5 km/h","C": "3 km/h","D": "3.5 km/h"},"correct_answer": "B"},{"id": 47,"difficulty": "hard","question": "The sum of a number and its reciprocal is 10/3. Find number. 🔄","options": {"A": "3","B": "1/3","C": "3 or 1/3","D": "2 or 1/2"},"correct_answer": "C"},{"id": 48,"difficulty": "hard","question": "A man sold a table at 10% profit and chair at 20% profit, getting ₹760. If sold at 20% profit on table and 10% on chair, get ₹770. Find cost prices. 🪑","options": {"A": "Table ₹400, Chair ₹300","B": "Table ₹500, Chair ₹200","C": "Table ₹300, Chair ₹400","D": "Table ₹200, Chair ₹500"},"correct_answer": "B"},{"id": 49,"difficulty": "hard","question": "The sum of ages of father and son is 50. 5 years ago, father was 7 times as old. Find age of father when son was born. 👨‍👦","options": {"A": "25","B": "28","C": "30","D": "32"},"correct_answer": "C"},{"id": 50,"difficulty": "hard","question": "The difference between two numbers is 5. Difference of their squares is 55. Find numbers. ➖","options": {"A": "8, 3","B": "9, 4","C": "10, 5","D": "11, 6"},"correct_answer": "A"},{"id": 51,"difficulty": "hard","question": "A man can row 15 km downstream and 9 km upstream in 3 hours. Also 20 km downstream and 12 km upstream in 4 hours. Find rowing speed in still water. 🚣","options": {"A": "8 km/h","B": "9 km/h","C": "10 km/h","D": "11 km/h"},"correct_answer": "A"},{"id": 52,"difficulty": "hard","question": "The sum of digits of a two-digit number is 7. Number obtained by interchanging digits exceeds original by 27. Find number. 🔄","options": {"A": "25","B": "34","C": "43","D": "52"},"correct_answer": "A"},{"id": 53,"difficulty": "hard","question": "Two blends of tea costing ₹300/kg and ₹375/kg mixed to get 15 kg mixture sold at ₹345/kg with 10% profit. Find quantity of cheaper tea. 🍵","options": {"A": "6 kg","B": "7 kg","C": "8 kg","D": "9 kg"},"correct_answer": "D"},{"id": 54,"difficulty": "hard","question": "A number of three digits has hundred's digit twice ten's digit. Sum of digits is 18. If digits reversed, number decreases by 396. Find number. 🔢","options": {"A": "864","B": "756","C": "648","D": "972"},"correct_answer": "A"},{"id": 55,"difficulty": "hard","question": "A invested ₹x and B ₹y in business. A's profit is 1/5 of total profit ₹P. If A invested ₹y and B ₹x, profit would be ₹(P-6000). Find x:y. 💼","options": {"A": "2:1","B": "3:1","C": "4:1","D": "5:1"},"correct_answer": "B"},{"id": 56,"difficulty": "hard","question": "A man travels 600 km partly by train and car. If he travels 120 km by train and rest by car, takes 8 hours. If 200 km by train and rest by car, takes 8 hours 20 minutes. Find train speed. 🚂","options": {"A": "60 km/h","B": "70 km/h","C": "80 km/h","D": "90 km/h"},"correct_answer": "A"},{"id": 57,"difficulty": "hard","question": "The sum of digits of a two-digit number is 12. If number is divided by digit sum, quotient is 6 and remainder 0. Find number. 🔢","options": {"A": "48","B": "57","C": "66","D": "75"},"correct_answer": "C"},{"id": 58,"difficulty": "hard","question": "A man buys 5 horses and 10 cows for ₹10,000. He sells horses at 15% profit and cows at 10% profit, earning ₹1150 profit. Find cost of a cow. 🐄","options": {"A": "₹400","B": "₹500","C": "₹600","D": "₹700"},"correct_answer": "B"},{"id": 59,"difficulty": "hard","question": "The perimeter of a rectangular field is 100 m. If length decreased by 2 m and breadth increased by 3 m, area increases by 44 m². Find original area. 📏","options": {"A": "500 m²","B": "525 m²","C": "550 m²","D": "575 m²"},"correct_answer": "D"},{"id": 60,"difficulty": "hard","question": "The sum of digits of a two-digit number is 8. If 36 is subtracted, digits reverse. Find number. 🔄","options": {"A": "53","B": "62","C": "71","D": "80"},"correct_answer": "B"}]}