# Ratio & Proportion (6)

1. If 6 years are subtracted from the present age of Ajay and the remainder is divided by 18, then the present age of Rahul is obtained. If Rahul is 2 years younger to Denis whose age is 5 years, then what is Ajay ‘s present age?
1. 50 years
2. 60 years
3. 55 years
4. 62 years

Explanation :-

Present age of Denis = 5 years
Present age of Rahul = 5 – 2 = 3 years
Let present age of Ajay = x years
Therefore, present age of Rahul = (x – 6)/18
[ (x – 6)/18 ] = 3
x – 6 = 18 * 3
x = 60
Ajay ‘s present age = 60 years

2. The ratio of the age of a man and his wife is 4:3. At the time of marriage the ratio was 5:3 and After 4 years this ratio will become 9:7. How many years ago were they married?
1. 8 years
2. 10 years
3. 11 years
4. 12 years

Explanation :-

Let the Present age of man = 4x &  Present age of his wife = 3x
According to Question, After 4 years
(4x + 4)/ (3x + 4) = 9/7
7(4x + 4) = 9(3x + 4)
x = 8
Therefore , Man’s Present age = 4*8 = 32 his wife’s Present age = 3*8 = 24
His wife’s Present age = 3*8 = 24
Let they were married y years ago , then
(32 – y)/ (28 – y) = 5/3
5(32 – y) = 3(28 – y)
y = 12

3. The product of the ages of Syam and Sunil is 240. If twice the age of Sunil is more than Syam’s age by 4 years, what is Sunil’s age?
1. 16
2. 14
3. 12
4. 10

Explanation :-

Let the Age of Shyam = x years   &   Age of Sunil = y years
According to Question
xy = 240     => x = 240/y
&
2y = x + 4  => 2y = (240/y) + 4
(2y)^2 = 240 + 4y
(y^2) – 2y – 120 = 0
y = 12   or     y = -10
Negative value is neglected because age cannot be negative
Therefore Sunil’s present age = 12 years

4. One year ago, the ratio of Sooraj’s and Vimal’s age was 6: 7 respectively. Four years hence, this ratio would become 7: 8. How old is Vimal?
1. 32
2. 34
3. 36
4. 38

Explanation :-

Let Sooraj’s age 1 year ago = 6x and Vimal’s age 1 year ago = 7x
After 4 years, Sooraj’s age = 6x + 5  &  Vimal’s age = 7x + 5
(65(758
(65(75)
4840 4935
x = 5
Vimal’s present age = 7x + 1 = (7*5) + 1 = 36 years

5. The total age of A and B is 12 years more than the total age of B and C. C is how many year younger than A?
1. 10
2. 11
3. 12
4. 13