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Monday, 29 April 2019

MATHS SOLVED IN STEPS: Age Related Problems - 04

28. The present ages of A,B and C are in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. What are their present ages (in years)?
A. Insufficient data    B. 16, 30, 40
C. 16, 28 40                  D. 16, 28, 36
Answer : Option D
Explanation :
Let's take the present age of A,B and C as 4x, 7x and 9x respectively
Then (4x - 8) + (7x – 8) + (9x – 8) = 56
=> 20x = 80
=> x = 4
Hence the present age of A, B and C are 4×4,
7×4 and 9×4 respectively
ie, 16,28 and 36 respectively.


29. A person's present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. What is the present age of the mother?
A.60     B. 50     C. 40     D.30
Answer : Option C
Explanation :
Let the present age of the person = x .
Then present age of the mother = 5x/2
Given that , after 8 years, the person will be onehalf of the age of his mother.
=> (x + 8) = (1/2)(5x/2 + 8)
=> 2x + 16 = 5x/2 + 8
=> x/2 = 8
=> x = 16
Present age of the mother = 5x/2 = 5×16/2 = 40

30. A is as much younger than B and he is older than C. If the sum of the ages of B and C is 50 years, what is definitely the difference between B and A's age?
A. Inadequate data    B. 3           C. 2               D. 5
Answer : Option A
Explanation :
Age of C < Age of A < Age of B
Given that sum of the ages of B and C is 50 years.
=> Let's take B's age = x and C's age = 50-x
Now we need to find out B's age – A's age. But we cannot find out this with the given data.


31. Sobha's father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?
A. 6     B. 5   C. 4    D. 12
Answer : Option A
Explanation :
Let Sobha's age = x and her brother's age = x-4
Then Sobha's father's age = x + 38
Sobha's mother's age = (x-4) + 36
=> Sobha's father's age - Sobha's mother's age = (x + 38) – [(x-4) + 36]
= x + 38 –x +4 – 36 = 6

32. The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age will be twice that of his son. What is the ratio of their present ages?
A. 7 : 3     B. 3 : 7       C. 9 : 4     D.4 : 9
Answer : Option A
Explanation :
Let the age of the son before 10 years = x and age of the father before 10 years = 3x
Now we can write as (3x + 20) = 2(x + 20)
=> x = 20
=> Age of Father the son at present = x + 10 = 20 + 10 = 30
Age of the father at present = 3x + 10 = 3×20 + 10 = 70
Required ratio = 70 : 30 = 7 : 3

33. The ages of two persons differ by 16 years. 6 years ago, the elder one was 3 times as old as the younger one. What are their present ages of the elder person?
A.10     B. 20     C. 30     D.40
Answer : Option C
Explanation :
Let's take the present age of the elder person = x  and the present age of the younger person = x – 16 (x – 6) = 3 (x-16-6)
=> x – 6 = 3x – 66
=> 2x = 60
=> x = 60/2 = 30

34. The present age of a father is 3 years more than three times the age of his son. Three years hence, father's age will be 10 years more than twice the age of the son. What is father's present age?
A.30     B.31     C. 32   D.33
Answer : Option D
Explanation :
Let the present age the son = x.
Then present age of the father = 3x + 3
Given that ,three years hence, father's age will be 10 years more than twice the age of the son
=> (3x+3+3) = 2(x + 3) +10
=> x = 10
Father's present age = 3x + 3 = 3×10+ 3 = 33


35. Kamal was 4 times as old as his son 8 years ago. After 8 years, Kamal will be twice as old as his son. Find out the present age of Kamal.
A.40     B.38     C. 42   D.36
Answer : Option A
Explanation :
Let the age of the son before 8 years = x.
Then age of Kamal before 8 years ago = 4x
After 8 years, Kamal will be twice as old as his son
=> 4x + 16 = 2(x + 16)
=> x = 8
Present age of Kamal = 4x + 8 = 4×8 +8 = 40
* MATHS (SOLVED IN STEPS ==> Ratio and Proportion
* MATHS (SOLVED IN STEPS ==> Progressions
* MATHS (SOLVED IN STEPS ==> Percentage
* MATHS (SOLVED IN STEPS ==> Surds and Indices
* MATHS (SOLVED IN STEPS ==> Calendar
* MATHS (SOLVED IN STEPS ==> Square and cube
* MATHS (SOLVED IN STEPS ==> Simplification
* MATHS (SOLVED IN STEPS ==> Problems on Average
* MATHS (SOLVED IN STEPS ==> HCF & LCM 
* MATHS (SOLVED IN STEPS ==> Profit and Loss
* MATHS (SOLVED IN STEPS ==> Problems on Trains 
* MATHS (SOLVED IN STEPS ==> Pipe and Cisterns
* MATHS (SOLVED IN STEPS ==> ODD MAN
* MATHS (SOLVED IN STEPS ==> TIME & WORK



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