Problems on Ages

A = B + 16. Also (1/2)B = (1/3)A, so A = 1.5B. Equating: B + 16 = 1.5B, 0.5B = 16, B = 32. Then A = 32 + 16 = 48.

The equations are: H + 2W + 3D = 85; 2H + 4W + 6D = 170; 5H + 10W + 15D = 450. The second equation is just 2 times the first. However, the third equation is 5 times the first, which would be 5H + 10W + 15D = 425. Since 425 != 450, the system is inconsistent and has 0 solutions.

Daughter is 20. Mother is 2*20 = 40. Father is 40 + 3 = 43. When the daughter was born (20 years ago), the father's age was 43 - 20 = 23.

Let M and D be current ages. M+D=45. Five years ago: (M-5)(D-5) = 4(M-5). Since M-5 is not zero, D-5 = 4, so D = 9. Then M = 45 - 9 = 36.

Let x be the number of years. The ratio equation is (14 + x) / (10 + x) = 5 / 4. Cross-multiplying gives 4(14 + x) = 5(10 + x), which simplifies to 56 + 4x = 50 + 5x, resulting in x = 6.

Let Anita's age be x. Sunita's age is 6x - 2. Five years later, their ages are x+5 and 6x+3. Their product is (x+5)(6x+3) = 330. Solving 6x^2 + 33x + 15 = 330 leads to 6x^2 + 33x - 315 = 0, or 2x^2 + 11x - 105 = 0. Factoring gives (2x + 21)(x - 5) = 0, so x = 5. Sunita's present age is 6(5) - 2 = 28. When Anita was born (5 years ago), Sunita was 28 - 5 = 23.

Let Rohan's age be x. Mother's age is x + 26. In 3 years, ages are x + 3 and x + 29. (x + 3)(x + 29) = 360 => x^2 + 32x + 87 = 360 => x^2 + 32x - 273 = 0. Factoring gives (x + 39)(x - 7) = 0. So x = 7.

Let son's age be x. Father's age = x^2. Equation: x^2 + 5x = 66. x^2 + 5x - 66 = 0. (x + 11)(x - 6) = 0. x = 6. Father's age = 6^2 = 36.

Let sister's age be x, girl's age be 2x. Four years later, (x+4)(2x+4) = 160. 2x^2 + 12x + 16 = 160, so 2x^2 + 12x - 144 = 0, or x^2 + 6x - 72 = 0. Solving (x+12)(x-6) = 0, we get x=6.

Let age be x. (x-5)(x+9) = 15. x^2 + 4x - 45 = 15. x^2 + 4x - 60 = 0. (x+10)(x-6) = 0. Age is 6. 3 years from now, age is 6+3 = 9.

The six sons have a total age of 6 x 8 = 48 years. The total age of the eight family members is 8 x 22 = 176 years, so the parents together are 128 years old. With the father 8 years older, the mother's age is 60 years.

Sum of ages of 4 persons 5 years ago was 45 * 4 = 180. Their present sum is 180 + (4 * 5) = 200. With the 5th person, the present sum is 49 * 5 = 245. The 5th person's age is 245 - 200 = 45.

Three years ago, the sum of ages of A, B, and C was 27 * 3 = 81. Their present sum is 81 + 3*3 = 90. Five years ago, the sum of B and C was 20 * 2 = 40. Their present sum is 40 + 5*2 = 50. A's present age is 90 - 50 = 40.

Let K be Kirti's age at marriage. Today, her age is K + 6. Given K + 6 = (5/4)K, we find (1/4)K = 6, so K = 24. Her current age is 24 + 6 = 30. Her son's age is (1/10) * 30 = 3 years.