Ages — Set #1 | Practice

{"setId":"b2ff8d48-7a91-4b68-9af7-4a5c53dafd0e","setTitle":"Classic Problems","topicName":"Ages","topicSlug":"ages","setNumber":1,"totalQuestions":10,"questions":[{"id":"d78489b9-1123-4145-8e6f-9adb20549c92","order":1,"statement":"The present age of a father is 3 times the age of his son. After 12 years, the father's age will be twice the age of his son. What is the present age of the son?","options":{"A":"12 years","B":"10 years","C":"14 years","D":"15 years"},"correctOption":"A","solution":"Let son's age = x, father's age = 3x. After 12 years: 3x+12 = 2(x+12). Solving: 3x+12 = 2x+24, so x = 12. Son's present age = 12 years."},{"id":"9d972bc8-caf0-41d8-b37e-2b4ff78ef98b","order":2,"statement":"Five years ago, Rahul was thrice as old as his son. Ten years hence, Rahul will be twice as old as his son. What is Rahul's present age?","options":{"A":"35 years","B":"40 years","C":"45 years","D":"50 years"},"correctOption":"D","solution":"Let son's age 5 years ago = x, Rahul's age 5 years ago = 3x. Ten years hence: (3x+5+10) = 2(x+5+10). So 3x+15 = 2x+30, giving x = 15. Rahul's present age = 3x+5 = 50 years."},{"id":"236e8fc6-85ef-40cb-9281-5a9845269d9c","order":3,"statement":"The ratio of the present ages of A and B is 4:5. After 8 years, the ratio of their ages will be 5:6. What is B's present age?","options":{"A":"32 years","B":"36 years","C":"40 years","D":"28 years"},"correctOption":"C","solution":"Let ages be 4x and 5x. After 8 years: (4x+8)/(5x+8) = 5/6. Cross multiply: 6(4x+8) = 5(5x+8), so 24x+48 = 25x+40, giving x = 8. B's present age = 5x = 40 years."},{"id":"766ee252-358c-4a20-aab1-f4e8750eac46","order":4,"statement":"The sum of the present ages of a mother and her daughter is 50 years. Five years ago, the mother's age was 9 times the age of the daughter. What is the present age of the daughter?","options":{"A":"9 years","B":"10 years","C":"11 years","D":"8 years"},"correctOption":"A","solution":"Let daughter's present age = d, mother's = 50-d. Five years ago: (50-d-5) = 9(d-5). So 45-d = 9d-45, giving 90 = 10d, d = 9. Daughter's present age = 9 years."},{"id":"3a669821-2c06-44de-89ab-7756601894d6","order":5,"statement":"A's present age is twice the age B was two years ago. The difference between their present ages is 2 years. What is A's present age?","options":{"A":"6 years","B":"8 years","C":"10 years","D":"12 years"},"correctOption":"B","solution":"Let B's age two years ago = x, so A's present age = 2x and B's present age = x+2. Difference: 2x-(x+2) = 2, so x = 4. A's present age = 2x = 8 years."},{"id":"2d5501fd-2e42-483f-b6a3-6da23141d20b","order":6,"statement":"The average age of a class of 30 students is 15 years. If the teacher's age is included, the average becomes 16 years. What is the teacher's age?","options":{"A":"45 years","B":"46 years","C":"44 years","D":"48 years"},"correctOption":"B","solution":"Total age of 30 students = 30*15 = 450. With teacher, total people = 31 and average = 16, so total age = 31*16 = 496. Teacher's age = 496-450 = 46 years."},{"id":"8746476f-d526-47d8-8824-70768c4fd804","order":7,"statement":"Ten years ago, the age of a father was four times the age of his son. Ten years hence, the father's age will be twice the age of his son. What is the ratio of their present ages?","options":{"A":"5:2","B":"7:3","C":"5:3","D":"3:1"},"correctOption":"A","solution":"Let son's age 10 years ago = x, father's = 4x. Ten years hence: (4x+10+10) = 2(x+10+10). So 4x+20 = 2x+40, giving x = 10. Present son's age = x+10 = 20, present father's age = 4x+10 = 50. Ratio = 50:20 = 5:2."},{"id":"a627c47f-2a8f-49ce-8120-849d3328c8d1","order":8,"statement":"The present ages of P and Q are in the ratio 3:4. Eight years from now, the ratio of their ages will be 4:5. What is P's present age?","options":{"A":"20 years","B":"24 years","C":"28 years","D":"32 years"},"correctOption":"B","solution":"Let ages be 3x and 4x. After 8 years: (3x+8)/(4x+8) = 4/5. Cross multiply: 5(3x+8) = 4(4x+8), so 15x+40 = 16x+32, giving x = 8. P's present age = 3x = 24 years."},{"id":"2a555a10-7f77-4de5-9edd-f9bda6e04aa8","order":9,"statement":"A man's present age is 125% of what it was 10 years ago, but only 83.33% of what it will be after 10 years. What is his present age?","options":{"A":"50 years","B":"55 years","C":"60 years","D":"65 years"},"correctOption":"A","solution":"Let present age = x. From the first condition: x = 1.25(x-10), so x = 1.25x-12.5, giving 0.25x = 12.5, x = 50. Check: age after 10 years = 60, and 83.33% of 60 = 50, which matches. Present age = 50 years."},{"id":"4abd95b6-4fff-4a56-b1a8-721a99eff73b","order":10,"statement":"The sum of the present ages of a father and his two children is 70 years. Five years ago, the father's age was four times the sum of the children's ages at that time. What is the father's present age?","options":{"A":"49 years","B":"45 years","C":"50 years","D":"44 years"},"correctOption":"A","solution":"Let father's present age = F, sum of children's present ages = S, so F+S = 70. Five years ago: father's age = F-5, sum of children's ages = S-10 (5 years less for each of the 2 children). Given F-5 = 4(S-10) = 4S-40, so F = 4S-35. Substituting: 4S-35+S = 70, giving 5S = 105, S = 21, and F = 49. Father's present age = 49 years."}]}