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Word Problems

Description: this is a test for reasoning
Number of Questions: 25
Created by:
Tags: Problems on Ages Linear Equations Quantitative Ability Algebra
Attempted 0/25 Correct 0 Score 0

The sum of the ages of X and Y is 45 years, the sum of the ages of Y and Z is 55 years. And the sum of the ages of X and Z is 65 years. What is the age of Y in years?

  1. 17.5

  2. 27.5

  3. 37.5

  4. 19.5

  5. none


Correct Option: A
Explanation:

X + Y = 45 (1) Y + Z = 55 (2)
X + Z = 65 (3) (X + Z) – (X + Y) = 65 – 45 [Equation(2) – (1)] = Z – Y = 20 (4) (Z – Y) + (Z + Y) = 20 + 55 [Equation(4) + (2)] = 2Z = 75 = Z = 37.5 Y + 37.5 = 55 (Substituting the value of Z in equation 2) = Y = 17.5

A father is twice as old as his son. Twenty years ago, the age of the father was 12 times the age of the son. The present age of the father is

  1. 44 years

  2. 32 years

  3. 22 yrs

  4. 45 years


Correct Option: A
Explanation:

Let son be x years old. Father = 2x 20 years ago, son = x - 20 father = 2x - 20 2x - 20 = 12*(x - 20) 2x - 20 = 12x - 240 Add 20 to both sides. 2x = 12x - 240 + 20 2x = 12x - 220 Add - 12x to both sides. 2x - 12x = 12x - 12x - 220 -12x + 2x = -240 + 20 -10x = -220 Divide by -10. x = -220/-10 x = 22 (son's age) Father's age = 2*22 = 44 years

The ratio between the present the ages of A and B is 4:5. If the difference between their present ages is 8 years, what is the sum of their present ages?

  1. 32

  2. 40

  3. 68

  4. 72

  5. None


Correct Option: D
Explanation:

Let the present ages of A and B be 4x and 5x, respectively. = 4x - 5x = 8 = x = 8 Now, present age of A is (4x) 32 and B is (5x) is 40. = 40 + 32 = 72.

The age of a man is 3 times of his son. 15 year ago, the man was 9 times as old as his son. What will the age of the man after 15 year?

  1. 45 year

  2. 60 year

  3. 75 year

  4. 65 year


Correct Option: C
Explanation:

"the man is 3 times as old as his son" ___ f = 3s "15 years ago, the man was 9 times as old as his son was then" ___ f - 15 = 9(s - 15) substituting ___ 3s - 15 = 9(s - 15) distributing ___ 3s - 15 = 9s - 135 adding 135 - 3s ___ 120 = 6s dividing by 6 ___ 20 = s substituting ___ f = 3(20) = 60 Therefore, after 15 years, the age of the man will be = 60 + 15 = 75 years.

The difference in the present ages of Jhadhav and Vijay is 24 year and their ages are in the ratio 3:7. What is the sum of their present ages?

  1. 48

  2. 60

  3. 66

  4. Cannot be determined

  5. none


Correct Option: B
Explanation:

Let the present ages of Jhadhav and Vijay be 3x and 7x, respectively. = 7x – 3x = 24 = x = 24/4 = 6 Therefore, the present ages of Jhadhav and Vijay are 42 and 18, respectively. = Sum of their ages = 42 + 18 = 60

The ratio of P's and Q's ages is 5:7. If difference between the present age of Q and the age of P six years hence is 2, then what is the total of present ages of P and Q

  1. 52

  2. 48

  3. 56

  4. Data inadequate


Correct Option: D

The present age of three persons are in the proportion of 4:7:9. Eight year ago, the sum of their ages was 56. Find their present ages.

  1. 20,35,45

  2. 8,20,28

  3. 16,28,36

  4. None of these


Correct Option: C

The ratio between the present ages of P and Q is 5:8. After four year, the ratio between their ages will be 2:3. What is Q’s age at present?

  1. 36

  2. 20

  3. 24

  4. 32

  5. none


Correct Option: D
Explanation:

Let the present ages of P and Q be 5x and 8x, respectively. (5x + 4)/(8x + 4) = 2/3 = 3(5x + 4) = 2(8x + 4) = 15x + 12 = 16x + 8 = x = 4 Therefore, the present age of Q = 8x = 32.

Five year ago, the age of a man was seven times the age of his son. The age of the man will be three times the age of his son in five year from now. The present age of the man and his son respectively are

  1. 68 year and 14 year

  2. 55 year and 15 year

  3. 54 year and 12 year

  4. 40 year and 10 year


Correct Option: D
Explanation:

Let present age of son = x Age of son before 5 years = x - 5 So, Present age of father = 7(x - 5) + 5 ……… (i) Age of son after 5 years = x + 5 Age of father after 5 years = 3(x + 5) So, present age of father = 3(x + 5) - 5 ……….(ii) Equating age of father, i.e. (i) and (ii):  7(x - 5) + 5 = 3(x + 5) - 5 7x – 35 + 5 = 3x + 15 - 5 7x - 3x = 15 - 5 + 35 - 5 4x = 40 x = 40/4. x (son) = 10, Father (3(10 + 5) - 5) =  40 years

The ratio between the present ages of A and B is 4:5. If the ratio between their ages four years hence becomes 14:17, what is the B's age at present?

  1. 30

  2. 28

  3. 34

  4. Data inadequate


Correct Option: A

Shivani’s mother was three times older than Shivani, 5 years ago. After 5 year she will be twice as old as Shivani. How old is Shivani today?

  1. 5 year

  2. 15 year

  3. 10 year

  4. 12 year


Correct Option: B

A father is twice as old as his son. 20 years back, he was twelve times as old as the son. What are their present ages?

  1. 24,12

  2. 44,22

  3. 48,24

  4. None of these


Correct Option: B

The present age of the father and the son are together 46 year. 5 year ago, the father was 11 times as old as his son. The age of the son after 5 year will be

  1. 13

  2. 14

  3. 12

  4. 11


Correct Option: A

The sum of the present age of the father and the son is 60 years. Six year ago, the father was 5 times as old as his son. The age of the son after 6 year will be

  1. 20

  2. 14

  3. 12

  4. 18


Correct Option: A

The ratio of Nutan’s age to Vidhya’s age at present is 5:4. If the sum of their ages at present is 36 year, what is Vidhya’s age at present in years?

  1. 20

  2. 16

  3. 24

  4. 12

  5. None of these


Correct Option: B

Sonu's father is 5 times as old as Sonu”. After 8 years his age will be thrice Sonu's age at that time. Find their present age?

  1. 30 year, 6 year

  2. 35 year, 7 year

  3. 40 year, 8 year

  4. 45 year, 9 year


Correct Option: C

Father’s age is 4 times that of his son. 5 years back, it was 7 times. His age now is

  1. 30

  2. 35

  3. 40

  4. 45


Correct Option: C
Explanation:

Let the present age of the son be x. Therefore, the present age of the father is 4x. 5 years ago, 7(x – 5) = (4x – 5) = 7x – 35 = 4x - 5 = 3x = 30 = x = 10 Therefore, the present age of the father is 4x = 40 years.

The present age of A and B are in the ratio of 3:5. Six years hence, the ratio will become 2:3. What is B's present age?

  1. 18

  2. 24

  3. 28

  4. 30


Correct Option: D

The sum of the ages of a father and son is 45 years. Five year ago the product to their ages was four times the father's age that time. The present age of the father and son respectively are?

  1. 39 year and 6 year

  2. 36 year and 9 year

  3. 25 year and 10 year

  4. None


Correct Option: B

The ratio between the ages of A and Q four years ago was 5:6. If the total of their ages at present is 52 year, what is the ratio of their present ages?

  1. 4:5

  2. 8:9

  3. 7:8

  4. 6:7

  5. None of these


Correct Option: D
Explanation:

Let the ages of A and Q be 5x and 6x, respectively. Now, (5x + 4) + (6x + 4) = 52 5x + 4 + 6x + 4 = 52 11x + 8 = 52 x = 4 Therefore, present age of A (5x) = 24 years and Q (6x) = 28 = Ratio of their present ages is 24 : 28 = 6 : 7

A mother after 4 years will be twice the age of her daughter. The sum of their age is 46. What is the present age of the daughter?

  1. 14

  2. 15

  3. 16

  4. None of these


Correct Option: A

The present ratio of the ages of P and Q is 2:3. If the age P is 12 years less than the age of Q, what is the present age of Q in years?

  1. 24

  2. 30

  3. 32

  4. 36

  5. None of these


Correct Option: D

The ages of Ram and Shyam are in the ratio. 2:1. After five year, the ratio of their ages will be 3:2. Their present ages are

  1. 20 and 10

  2. 10 and 5

  3. 15 and 5

  4. 40 and 20


Correct Option: B

Father is 5 year older than the mother and the mother’s age now is thrice the age of the daughter. The daughter is now 10 year old. What was the age of father when the daughter was born?

  1. 20 years

  2. 15 years

  3. 25 years

  4. 30 years


Correct Option: C

If the sum of ages of P and Q is 55 years, and the difference between Q and P’s ages is 5 years, what is Q’s present age?

  1. 25

  2. 30

  3. 24

  4. Data inadequate

  5. None


Correct Option: B
Explanation:

P + Q = 55 (1) -P + Q = 5 (2) (P + Q) + (-P + Q) [Adding (1) and (2)] = 2Q = 60 = Q = 30

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