PlacementPrep10 years ago, the ages of A and B were in the ratio 3 : 5. Today A is 22 years old. How old is B now?
Solution
10 years ago A was 12 = 3k, so k = 4.
B then was 5 × 4 = 20, so B now = 20 + 10 = 30.
Answer: (A) 30 years
Quantitative Aptitude · Arithmetic
Problems on Ages: placement practice questions
30 moderate questions in the pattern of campus placement tests. Pick an option to check your answer, then open the step-by-step solution.
The ages of two brothers are in the ratio 4 : 5 and differ by 6 years. What is the age of the elder brother?
Solution
Difference of ratio parts = 1, which is 6 years, so one part = 6.
Elder = 5 × 6 = 30 years.
Answer: (D) 30 years
3 years ago, the ages of A and B were in the ratio 3 : 5. Today A is 24 years old. How old is B now?
Solution
3 years ago A was 21 = 3k, so k = 7.
B then was 5 × 7 = 35, so B now = 35 + 3 = 38.
Answer: (D) 38 years
The ages of two brothers are in the ratio 6 : 5 and differ by 4 years. What is the age of the elder brother?
Solution
Difference of ratio parts = 1, which is 4 years, so one part = 4.
Elder = 6 × 4 = 24 years.
Answer: (B) 24 years
8 years ago, the ages of A and B were in the ratio 4 : 5. Today A is 32 years old. How old is B now?
Solution
8 years ago A was 24 = 4k, so k = 6.
B then was 5 × 6 = 30, so B now = 30 + 8 = 38.
Answer: (D) 38 years
The ages of two brothers are in the ratio 5 : 7 and differ by 12 years. What is the age of the elder brother?
Solution
Difference of ratio parts = 2, which is 12 years, so one part = 6.
Elder = 7 × 6 = 42 years.
Answer: (B) 42 years
The ages of two brothers are in the ratio 2 : 5 and differ by 21 years. What is the age of the elder brother?
Solution
Difference of ratio parts = 3, which is 21 years, so one part = 7.
Elder = 5 × 7 = 35 years.
Answer: (B) 35 years
4 years ago, the ages of A and B were in the ratio 2 : 5. Today A is 20 years old. How old is B now?
Solution
4 years ago A was 16 = 2k, so k = 8.
B then was 5 × 8 = 40, so B now = 40 + 4 = 44.
Answer: (D) 44 years
The ages of two brothers are in the ratio 3 : 2 and differ by 7 years. What is the age of the elder brother?
Solution
Difference of ratio parts = 1, which is 7 years, so one part = 7.
Elder = 3 × 7 = 21 years.
Answer: (A) 21 years
5 years ago, the ages of A and B were in the ratio 5 : 3. Today A is 30 years old. How old is B now?
Solution
5 years ago A was 25 = 5k, so k = 5.
B then was 3 × 5 = 15, so B now = 15 + 5 = 20.
Answer: (C) 20 years
The ages of two brothers are in the ratio 7 : 2 and differ by 25 years. What is the age of the elder brother?
Solution
Difference of ratio parts = 5, which is 25 years, so one part = 5.
Elder = 7 × 5 = 35 years.
Answer: (C) 35 years
9 years ago, the ages of A and B were in the ratio 2 : 5. Today A is 21 years old. How old is B now?
Solution
9 years ago A was 12 = 2k, so k = 6.
B then was 5 × 6 = 30, so B now = 30 + 9 = 39.
Answer: (A) 39 years
The ages of two brothers are in the ratio 3 : 2 and differ by 5 years. What is the age of the elder brother?
Solution
Difference of ratio parts = 1, which is 5 years, so one part = 5.
Elder = 3 × 5 = 15 years.
Answer: (B) 15 years
3 years ago, the ages of A and B were in the ratio 3 : 5. Today A is 15 years old. How old is B now?
Solution
3 years ago A was 12 = 3k, so k = 4.
B then was 5 × 4 = 20, so B now = 20 + 3 = 23.
Answer: (D) 23 years
4 years ago, the average age of a family of 6 members was 26 years. A baby has since been born, and the average age of the family today is still 26 years. How old is the baby?
Solution
Total age 4 years ago = 6 × 26 = 156; today these 6 members total 156 + 6 × 4 = 180.
With the baby, total = 7 × 26 = 182.
Baby's age = 182 − 180 = 2 years.
Answer: (C) 2 years
3 years ago, the average age of a family of 6 members was 20 years. A baby has since been born, and the average age of the family today is still 20 years. How old is the baby?
Solution
Total age 3 years ago = 6 × 20 = 120; today these 6 members total 120 + 6 × 3 = 138.
With the baby, total = 7 × 20 = 140.
Baby's age = 140 − 138 = 2 years.
Answer: (B) 2 years
A father is 5 times as old as his son. After 10 years he will be 3 times as old. What is the father's present age?
Solution
Let the son be s; father = 5s.
5s + 10 = 3(s + 10) gives s = 10, so father = 50.
Answer: (D) 50 years
5 years ago, the average age of a family of 4 members was 21 years. A baby has since been born, and the average age of the family today is still 21 years. How old is the baby?
Solution
Total age 5 years ago = 4 × 21 = 84; today these 4 members total 84 + 4 × 5 = 104.
With the baby, total = 5 × 21 = 105.
Baby's age = 105 − 104 = 1 years.
Answer: (A) 1 years
A father is 4 times as old as his son. After 6 years he will be 3 times as old. What is the father's present age?
Solution
Let the son be s; father = 4s.
4s + 6 = 3(s + 6) gives s = 12, so father = 48.
Answer: (C) 48 years
6 years ago, the average age of a family of 5 members was 32 years. A baby has since been born, and the average age of the family today is still 32 years. How old is the baby?
Solution
Total age 6 years ago = 5 × 32 = 160; today these 5 members total 160 + 5 × 6 = 190.
With the baby, total = 6 × 32 = 192.
Baby's age = 192 − 190 = 2 years.
Answer: (D) 2 years
5 years ago, the average age of a family of 6 members was 31 years. A baby has since been born, and the average age of the family today is still 31 years. How old is the baby?
Solution
Total age 5 years ago = 6 × 31 = 186; today these 6 members total 186 + 6 × 5 = 216.
With the baby, total = 7 × 31 = 217.
Baby's age = 217 − 216 = 1 years.
Answer: (A) 1 years
The sum of a father's and son's ages is 48. After 3 years, the father will be 2 times as old as the son. What is the son's present age?
Solution
Let son = s. Then (48 − s + 3) = 2(s + 3).
Solving: s = 15 years.
Answer: (C) 15 years
A father is 3 times as old as his son. After 10 years he will be 2 times as old. What is the father's present age?
Solution
Let the son be s; father = 3s.
3s + 10 = 2(s + 10) gives s = 10, so father = 30.
Answer: (D) 30 years
6 years ago, the average age of a family of 6 members was 37 years. A baby has since been born, and the average age of the family today is still 37 years. How old is the baby?
Solution
Total age 6 years ago = 6 × 37 = 222; today these 6 members total 222 + 6 × 6 = 258.
With the baby, total = 7 × 37 = 259.
Baby's age = 259 − 258 = 1 years.
Answer: (B) 1 years
The sum of a father's and son's ages is 58. After 6 years, the father will be 4 times as old as the son. What is the son's present age?
Solution
Let son = s. Then (58 − s + 6) = 4(s + 6).
Solving: s = 8 years.
Answer: (A) 8 years
The sum of a father's and son's ages is 56. After 5 years, the father will be 5 times as old as the son. What is the son's present age?
Solution
Let son = s. Then (56 − s + 5) = 5(s + 5).
Solving: s = 6 years.
Answer: (C) 6 years
5 years ago, the average age of a family of 5 members was 28 years. A baby has since been born, and the average age of the family today is still 28 years. How old is the baby?
Solution
Total age 5 years ago = 5 × 28 = 140; today these 5 members total 140 + 5 × 5 = 165.
With the baby, total = 6 × 28 = 168.
Baby's age = 168 − 165 = 3 years.
Answer: (C) 3 years
The sum of a father's and son's ages is 52. After 10 years, the father will be 2 times as old as the son. What is the son's present age?
Solution
Let son = s. Then (52 − s + 10) = 2(s + 10).
Solving: s = 14 years.
Answer: (C) 14 years
A father is 3 times as old as his son. After 7 years he will be 2 times as old. What is the father's present age?
Solution
Let the son be s; father = 3s.
3s + 7 = 2(s + 7) gives s = 7, so father = 21.
Answer: (D) 21 years
A father is 4 times as old as his son. After 12 years he will be 2 times as old. What is the father's present age?
Solution
Let the son be s; father = 4s.
4s + 12 = 2(s + 12) gives s = 6, so father = 24.
Answer: (B) 24 years
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