# Aptitude Problems on Ages Test Paper 4

16) The product of the ages of Shyam and Ram is 240. If double the age of Ram is more than Shyam's age by 4 years, what is Ram's present age?

1. 16
2. 14
3. 12
4. 10

Explanation:

: Let the age of Ram = X years
Age of Shyam = Y years
According to question
XY= 240 ............eq.1
And, 2X = Y + 4
Y= 2X- 4
Y = 2(X-2) ...............eq.2

Now putting the value of eq.2 in eq.1
X ×[ 2(X-2)] = 240
X × (2X - 4) =240
2X2 - 4X =240
X2- 2X = 120
X2 - 2X - 120 = 0

Doing the factors of above equation:
X2 - (12-10)X - 120 = 0
X2 -12X + 10X -120 = 0
X(X-12) + 10(X-12) = 0
(X-12) (X+10) = 0
X+10 = 0, X-12 = 0
X= -10, X = 12
Therefore Ram's age is 12 years.

17) The present ages of Arun, Sunil, and Vivek are in proportions 4:7:9. Before eight years, the sum of their ages was 56. What are their present ages in years?

1. Insufficient Data
2. 16,30,40
3. 16,28,40
4. 16,28,36

Explanation:
Let the ratio constant be x
Then the Present age of Arun, Sunil and Vivek would be 4x, 7x, 9x
Age before eight years:
4x-8, 7x-8, 9x-8
According to question
4x-8 + 7x-8 + 9x-8 = 56
20x = 80
x= 80/20
x= 4
Then their present is 4×4 = 16; 7×4= 28 and 9×4= 36 respectively.

18) The age of John 10 years ago was thrice the age of his son. After ten years, John's age will be twice that of his son. What is the ratio of their present ages?

1. 7:3
2. 3:7
3. 9:4
4. 4:9

Explanation:
Let the age of son 10 years ago = x years
Then age of John = 3x
According to question
After 10 years
2(x+20) = 3x+20
2x + 40 = 3x + 20
X= 20
The present of son and John are x+10 and 3x+ 10 respectively
Son's age = 20+10 = 30 years
John's age = 3 ×20 + 10 = 60+10 = 70 years
Ratio of their present age is =70:30 =7:3

19) 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 Shoba?s parents?

1. 6 Years
2. 5 Years
3. 4 Years
4. 3 Years

Explanation:
Let the age of Sobha be=x and
Her brother's age =x-4
Sobha's father's age =x+38
Sobha's mother's present age =(x-4)+36=x+32
Sobha's father's age - Sobha's mother's age
=(x+38) -(x+32) =6 Years

20) Vipul's present age is two-fifths of the age of his mother. After 8 years, Vipul will be one-half of the age of his mother. What is the present age of Vipul's mother?

1. 60 Years
2. 50 Years
3. 40 Years
4. 30 Years

Solution:
Let the present age of the Vipul =x
Then, the present age of the mother Given that, after 8 years, Vipul's will be one-half of the age of his mother.   X=16
So, the present age of the mother: Aptitude Problems on Ages Test Paper 1
Aptitude Problems on Ages Test Paper 2
Aptitude Problems on Ages Test Paper 3
Aptitude Problems on Ages Test Paper 5
Problems on Ages Concepts

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