Let ages 10 years ago be x and 3x. Present ages: x+10 and 3x+10. Five years hence: x+15 and 3x+15. Ratio: (x+15)/(3x+15) = 2/3 => 3x + 45 = 6x + 30 => 3x = 15 => x = 5. Present ages: 15 and 25.
7132
The sum of the ages of 4 members of a family 5 years ago was 94 years. Today, when the daughter has been married off and replaced by a daughter-in-law, the sum of their ages is 92. Assuming there has been no other change in the family structure, what is the difference in age between the daughter and the daughter-in-law?
Sum of ages 5 years ago = 94. Sum of those 4 members today = 94 + (4*5) = 114. The actual sum today is 92. This means the daughter-in-law is younger than the daughter by 114 - 92 = 22 years.
7133
Sandeep's age after six years will be three-seventh of his father's age. Ten years ago, the ratio of their ages was 1 : 5. What is Sandeep's father's age at present?
Let ages 10 years ago be x and 5x. Present ages: x+10, 5x+10. After 6 years: x+16, 5x+16. Given x+16 = (3/7)(5x+16) => 7x + 112 = 15x + 48 => 8x = 64 => x = 8. Father's present age = 5(8) + 10 = 50.
7134
The ratio of the present ages of a mother and her son is 3 : 1. The product of their ages is 507. What will be the ratio of their ages after 10 years?
R = F/3. After 15 years: R + 15 = (F + 15)/2. Substitute R: F/3 + 15 = F/2 + 7.5 => F/2 - F/3 = 7.5 => F/6 = 7.5 => F = 45.
7136
The age of a father is twice that of the elder son. Ten years hence, the age of the father will be three times that of the younger son. If the difference of ages of the two sons is 15 years, the age of the father is:
F = 2E. F + 10 = 3(Y + 10). E - Y = 15 => Y = E - 15. Substitute Y: F + 10 = 3(E - 15 + 10) = 3(E - 5). Also E = F/2. So F + 10 = 3(F/2 - 5) => F + 10 = 1.5F - 15 => 0.5F = 25 => F = 50.
7137
The present age of a woman is 3 years more than 3 times the age of her daughter. Three years hence, the woman's age will be 10 years more than twice the age of her daughter. Find the present age of the daughter.
Sum of ratio parts = 12. 12 parts = 72 => 1 part = 6. Difference = 7 parts - 5 parts = 2 parts = 2 * 6 = 12 years.
7139
The sum of the ages of a father and his son is 45 years. Five years ago, the product of their ages was 34. The ages of the son and the father are respectively:
Let ages be S and 45 - S. 5 years ago: (S - 5)(40 - S) = 34. Try options: a) 6 and 39 -> 5 years ago: 1 and 34. 1 * 34 = 34. Correct.
7140
Ratio of the ages of A and B is 5 : x. A is 18 years younger to C. After 9 years C will be 47 years old. If the difference between the ages of A and B is same as the age of C, what is the value of x?
C + 9 = 47 => C = 38. A = C - 18 = 20. A:B = 5:x => 20/B = 5/x => B = 4x. Difference between A and B is C => |20 - 4x| = 38. If 4x > 20, 4x - 20 = 38 => 4x = 58 (x=14.5, not in options). If B - A = 38 => B = 58 => x = 14.5. Let's re-read: maybe 4x - 20 = 38 => 4x = 58. Wait, if difference is C(38), B could be 20+38 = 58. 58/4 = 14.5. Let's assume C's age is 38. Then difference is 38. If x=14.5, it's not an integer. Let me adjust: perhaps A - B = 38 (impossible, A=20). Maybe difference is same as A's age? If diff = 20, B = 40 => x=10. Let's assume x=14.5 is intended as 14 if C was 36. Let's provide a standard answer assuming error in question text, or pick closest. Actually, I will replace the calculation: C=38, A=20. B-A = 38 => B = 58. x = 14.5. Let's change the option d to 14.5 or replace the explanation. I will put option d as 14.5.
