 # Ratio & Proportion (5)

1. 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?
1. 6 years
2. 5 years
3. 4 years
4. 3 years

Explanation :-

Lets suppose Sobha’s age= x
her brother’s age = x – 4
Sobha’s father’s age = x + 38
Sobha’s mother’s age = (x – 4) + 36 = x + 32
Sobha’s father’s age – Sobha’s mother’s age = (x + 38) – (x + 32) = 6 years

2. 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?
1. 7 : 3
2. 3 : 7
3. 9 : 4
5. 4 : 9

Explanation :-

Let the age of son 10 years ago = x years
Therefore Age of father 10 years ago =  3 x years
According to question ,
(3x + 10) + 10 = 2 [(x + 10) + 10] 3x + 20 = 2x + 40
x = 20.
Ratio of Present age of father and son  = (3x + 10) : (x + 10) = 70 : 30 = 7 : 3.

3. 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?
1. 10
2. 20
3. 30
4. 40

Explanation :-

Lets suppose  the age of younger person = x years,
Therefore,  Elder person’s  age = (x +16)
Before , 6 years
3(x-6) = (x+16-6)
3x-18 = x+10
x = 14.
So,  Elder person’s  age = x + 16 = 30

4. 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?
1. 30 years
2. 31 years
3. 32 yeas
4. 33 years

Explanation :-

Let the Son’s peresent Age = x.
Therefore, Father’s Present age = 3x + 3
After three years,
Son’s Age = (x+3) & Father’s Present age = (3x + 3 + 3) = (3x + 6)
Therefore , According to question,
(3x + 6) = 10 + 2(x + 3)
3x + 6 = 10 + 2x + 6
x = 10
Father’s Present age = 3x + 3 = 3*10 + 3 = 33

5. 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.
1. 40 years
2. 38 years
3. 42 years
4. 36 years

Explanation :-

Let Son’s age 8 years ago = x years
Therefore, Kamal’s age 8 years ago = 4x
After 8 years,
Son’s age = (x + 8 + 8 ) = (x +16) years
Kamal’s age = 4x + 8 + 8 = 4x +16
According to Question
416 (16)
x = 8
Kamal’s Present Age = 4x + 8 = (4 * 8) + 8 = 40 years