Quantitative Aptitude — Problems on Ages

Let the son's current age be 'S' years. Ravi's current age = 3S years. According to the problem, the sum of their ages is 48 years. Formula used: Linear Equation S + 3S = 48 4S = 48 S = 48 / 4 S = 12 years (Son's age) Ravi's age = 3S = 3 * 12 = 36 years. Therefore, Ravi's age is 36 years.

Let the current ages of P and Q be 5x and 7x years respectively. Concept used: Ratios and Differences Given, P is 10 years younger than Q, which means the difference in their ages is 10 years. 7x - 5x = 10 2x = 10 x = 10 / 2 x = 5 P's age = 5x = 5 * 5 = 25 years. Q's age = 7x = 7 * 5 = 35 years. Sum of their ages = P's age + Q's age = 25 + 35 = 60 years. Therefore, the sum of their ages is 60 years.

Let the present ages of A and B be A and B years respectively. Concept used: Ratios and Linear Equations 5 years ago: (A - 5) / (B - 5) = 2 / 3 3(A - 5) = 2(B - 5) 3A - 15 = 2B - 10 3A - 2B = 5 (Equation 1) 5 years from now: (A + 5) / (B + 5) = 3 / 4 4(A + 5) = 3(B + 5) 4A + 20 = 3B + 15 4A - 3B = -5 (Equation 2) Multiply Equation 1 by 3: 9A - 6B = 15 Multiply Equation 2 by 2: 8A - 6B = -10 Subtract the second modified equation from the first modified equation: (9A - 6B) - (8A - 6B) = 15 - (-10) 9A - 8A = 15 + 10 A = 25 Substitute A = 25 into Equation 1: 3(25) - 2B = 5 75 - 2B = 5 2B = 75 - 5 2B = 70 B = 35 So, the present age of A is 25 years and B is 35 years. Therefore, the present age of A is 25 years.

Let the son's current age be 'S' years. Let the father's current age be 'F' years. Concept used: Forming and solving linear equations based on age relationships. According to the first condition: F = 4S (Equation 1) In 5 years: Son's age will be S + 5. Father's age will be F + 5. According to the second condition: F + 5 = 3(S + 5) F + 5 = 3S + 15 F - 3S = 10 (Equation 2) Substitute F = 4S from Equation 1 into Equation 2: 4S - 3S = 10 S = 10 Now find the father's age using Equation 1: F = 4S = 4 * 10 = 40 years. Therefore, the present age of the father is 40 years.

Let the mother's current age be 'M' years and the daughter's current age be 'D' years. Concept used: System of Linear Equations According to the first condition: M + D = 50 (Equation 1) 5 years ago: Mother's age was M - 5. Daughter's age was D - 5. According to the second condition: M - 5 = 7(D - 5) M - 5 = 7D - 35 M - 7D = -30 (Equation 2) From Equation 1, M = 50 - D. Substitute this value of M into Equation 2: (50 - D) - 7D = -30 50 - 8D = -30 8D = 50 + 30 8D = 80 D = 80 / 8 D = 10 years (Daughter's age) Now substitute D = 10 into Equation 1: M + 10 = 50 M = 50 - 10 M = 40 years (Mother's age) Therefore, the present ages are Mother = 40 years and Daughter = 10 years.

Let the current ages of the two brothers be 3x and 5x years respectively. Concept used: Ratios and Proportions, Linear Equations After 6 years: First brother's age = 3x + 6 Second brother's age = 5x + 6 According to the problem, the ratio of their ages after 6 years will be 5:7. (3x + 6) / (5x + 6) = 5 / 7 Cross-multiply: 7(3x + 6) = 5(5x + 6) 21x + 42 = 25x + 30 Rearrange the terms to solve for x: 42 - 30 = 25x - 21x 12 = 4x x = 12 / 4 x = 3 Now, calculate their current ages: First brother's current age = 3x = 3 * 3 = 9 years. Second brother's current age = 5x = 5 * 3 = 15 years. Difference between their current ages = 15 - 9 = 6 years. Therefore, the difference between their current ages is 6 years.

Let the present age of the man be 'M' years. Let the sum of the present ages of his two children be 'S' years. Concept used: Forming and solving linear equations with multiple variables. According to the first condition: M = 2S (Equation 1) After 20 years: Man's age will be M + 20. Each child's age will increase by 20 years. Since there are two children, the sum of their ages will increase by 20 + 20 = 40 years. So, the sum of the children's ages after 20 years will be S + 40. According to the second condition: M + 20 = S + 40 (Equation 2) Substitute M = 2S from Equation 1 into Equation 2: 2S + 20 = S + 40 Solve for S: 2S - S = 40 - 20 S = 20 Now find the man's present age using Equation 1: M = 2S = 2 * 20 = 40 years. Therefore, the present age of the man is 40 years.

Let the person's current age be 'P' years and his father's current age be 'F' years. Concept used: Fractional relationships in age problems, Linear Equations. According to the first condition: P = (2/5)F (Equation 1) After 8 years: Person's age will be P + 8. Father's age will be F + 8. According to the second condition: P + 8 = (1/2)(F + 8) (Equation 2) Substitute P = (2/5)F from Equation 1 into Equation 2: (2/5)F + 8 = (1/2)F + 4 To eliminate fractions, multiply the entire equation by the least common multiple of 5 and 2, which is 10: 10 * [(2/5)F + 8] = 10 * [(1/2)F + 4] 4F + 80 = 5F + 40 Rearrange the terms to solve for F: 80 - 40 = 5F - 4F 40 = F So, the father's current age is 40 years. Therefore, the father's current age is 40 years.

Let the current ages of A and B be 4x and 5x years respectively. Concept used: Ratios and Differences, Sum of Ages. Given, the difference between their ages is 5 years. 5x - 4x = 5 x = 5 Now, calculate their current ages: A's current age = 4x = 4 * 5 = 20 years. B's current age = 5x = 5 * 5 = 25 years. Sum of their current ages = 20 + 25 = 45 years. After 5 years: A's age will be 20 + 5 = 25 years. B's age will be 25 + 5 = 30 years. Sum of their ages after 5 years = 25 + 30 = 55 years. Therefore, the sum of their ages after 5 years will be 55 years.