Problems on Ages

Ages are 4x and 5x. Difference is 5x - 4x = x = 7 years. Sum of ages = 4x + 5x = 9x = 9 × 7 = 63 years.

Let Raju's age = 5x, Sahil's age = 9x. Given 9x - 5x = 12, so 4x = 12, x = 3. Current ages: Raju = 15, Sahil = 27. After 21 years: Raju = 36, Sahil = 48. Ratio of Sahil to Raju = 48:36 = 4:3, which is option A.

Let present ages be 5x, 7x, 4x. Sum after 9 years: (5x+9)+(7x+9)+(4x+9)=16x+27=139, so 16x=112, x=7. Garima's present age = 7x = 49. Garima's age 5 years ago = 49-5 = 44 years. Let me verify: Tushar=35, Garima=49, Saurav=28. After 9 years: 44+58+37=139. Correct. The marked answer C (44 years) is correct.

Let ages 4 years ago be 4x and 3x. Present ages: (4x+4) and (3x+4). Sum = 7x+8, Difference = x. Given (7x+8)/(x) = 9/1, so 7x+8 = 9x, giving x = 4. Present ages: 20 and 16. Vimal is currently 16, so after 4 years, Vimal will be 20.

The ratios given are Ravi:Raj = 3:4 and Raj:Rahul = 7:8. To connect these, we need to find a common value for Raj. LCM of 4 and 7 is 28, so Ravi:Raj:Rahul = 21:28:32. After 1 year, ratios become 22:29:33. After 5 more years (6 years total), ages are 27k+6, 34k+6, 38k+6. Given Rahul-Ravi = 11 years: (38k+6)-(27k+6) = 11k = 11, so k=1. Ravi's age 10 years ago: (21+1)-10 = 12. Rahul's age 12 years later: (32+1)+12 = 45. Ratio = 12:45 = 4:15.

Let Raju's age be x. Father's age = 2x + 20. After 2 years: 2x + 22 = 3(x + 2). Solving: 2x + 22 = 3x + 6. Therefore x = 16. Father's age = 2(16) + 20 = 52 years. This matches option C.

Let ages 8 years ago be 9x and 10x. Present ages: 9x + 8 and 10x + 8. After 4 years: 9x + 12 and 10x + 12. Ratio is (9x + 12)/(10x + 12) = 12/13. Cross-multiply: 13(9x + 12) = 12(10x + 12) → 117x + 156 = 120x + 144 → 3x = 12 → x = 4. A's present age = 9(4) + 8 = 44. C's age = A's age + 6 = 50.

Let Jack's age = J and Jones' age = O. 6J = 5O, so O = 6J/5. After 10 years: (J+10) + (O+10) = 3J. Substituting O: J + 10 + 6J/5 + 10 = 3J. Multiplying by 5: 5J + 50 + 6J + 50 = 15J, so 11J + 100 = 15J, giving 4J = 100 and J = 25. Therefore O = 6 × 25/5 = 30 years.

Let present ages be 6x and 5x. Four years ago: (6x-4)/(5x-4) = 5/4. Cross-multiplying: 24x - 16 = 25x - 20, giving x = 4. Present ages: A = 24, B = 20. After 12 years: A = 36, B = 32. Ratio = 36:32 = 9:8.

Let son's age = x, father's age = 2x+6. In 4 years: (2x+10 + x+4)/2 = 34, so 3x+14 = 68, x = 18. Father = 2(18)+6 = 42. Ratio son:father = 18:42 = 3:7. Answer C is correct.

Three years ago, 5 members had average age 17, so total age was 5×17=85 years. Today (after 3 years), those 5 members are 3 years older each: 85+15=100 years. Current family has 6 members with same average (17 years), so total age is 6×17=102. Baby's age = 102-100=2 years.

Let present ages be P and Q. From 'sum of ages 8 years ago is 80': (P-8)+(Q-8)=80 → P+Q=96. From 'Q's age 14 years ago equals P's present age': Q-14=P → Q=P+14. Substituting: P+(P+14)=96 → 2P=82 → P=41. After 4 years, P will be 41+4=45 years. Option C (46) forgets to add 4 to the current age.

Let Romi's present age be x years. Then Nisha's present age is (x+15) years. Five years ago: Romi was (x-5) and Nisha was (x+10). Given (x+10)=3(x-5), solving gives x=12.5. Nisha's present age = 12.5+15=27.5 years.

Let ages be 3x, 5x, 2x. Sum: 3x + 5x + 2x = 100, giving x = 10. Manish = 30, Kamal = 50, Sohan = 20. Manish after 10 years = 40. Kamal before 6 years = 44. Ratio = 40:44 = 10:11.

7 years ago: 4x and 5x. 7 years hence: (4x+14)/(5x+14) = 5/6, solving gives x=6. Present ages: 31 and 37. After 5 years: 36 and 42, ratio = 6:7 = 30:35 = 34:41.