1**. **Six years ago Jose was twice as old as Joseph of the ratio of their present age is 9 : 5 respectively, what is the difference between their present ages? [Bank PO 2000]

**(a) **24

**(b) **30

**(c) **50

**(d) **none of these

**Answer: (a)**

**Explanation:**

Let their present ages be 9x and 5x**. **six years ago,

(9x-6)=2(5x-6) => x=6

The difference between their present ages = 9x-5x=4×6=24 years

2**. **Father’s age is 5 yrs more than mother’s age & mother’s age is 3 times of daughter’s age**. **The present age of daughter is 10 yrs**. **What was the age of father at daughter’s birth?

**(a) **20 yrs

**(b) **22 yrs

**(c) **25 yrs

**(d) **28 yrs

**Answer: (c)**

**Explanation:**

Present age of daughter= 10yrs

Mother= 10 ×3= 30yrs

Father= 30+5= 35yrs

So, father’s age while 10 yrs ago was 25 years.

3. 15 years hence a man will be 4 times as old as he was 15 years ago, His present age is?

**(a) **15

**(b) **20

**(c) **25

**(d) **30

**Answer: (c)**

**Explanation:**

Let us take present age of man is x years**.**

15+x=4(x-15)

15+x=4x-60

3x=75

x=25years

4. Sachin is elder than Rohit by 6 years**. **If their ages are in the ratio of 6:8, how old is Sachin?

**(a) **6 yrs

**(b) **8 yrs

**(c) **10 yrs

**(d) **18 yrs

**Answer: (d)**

**Explanation:**

Let Sachin age be x, Rohit age be x-6

8x= 6x-36

x= 18x

Sachin age= 18 yrs, Rohit age= 12 yrs

5**. **Present age ratio of x, y is 6:8, 7 years hence, the ages become 4:5**. **What is x’s present age?

**(a) **18

**(b) **20

**(c) **21

**(d) **25

**Answer: (c)**

**Explanation:**

After 7 years, (6m+7)/(8m+7)=4/5

30m+35=32m+28

2m=7

6. A father tells his eldest son, I’m thrice as old as your youngest sister and when I was as old as you, you were as old as youngest sister**. **If the youngest sister is 17 yrs old, how many years ago was her elder brother born?

**(a) **30 yrs ago

**(b) **32 yrs ago

**(c) **34 yrs ago

**(d) **36 yrs ago

**Answer: (c)**

**Explanation:**

Let, father is f, eldest son as s, youngest daughter as d

Given f= 3d, f = 3 x 17 =51;

Fathers age – some years (x) = Sons age; —>1

Sons age- some years(x) = daughters age =17; —>2

54 – x = sons age;

Sons age = 17 + x;

54 – x =17 +x;

x= 17;

Substituting x

Sons age =54-17 =34;

Son’s age is 34.

7**. **A said to B “I am twice as old as you were when I was as old you are now”. Sum of their ages is 42**. **Find their present ages**. **[Delhi police, 2007]

**(a) **12, 20

**(b) **18, 24

**(c) **16, 26

**(d) **17, 25

**Answer: (b)**

**Explanation:**

Clearly by choosing option (b) we see that A was equal to B’s age, i**. **e**. **18 years, 6 years ago and at that time B was 12 years old**. **So, A’s present age, 24 years, is twice of B’s that time of age, i**. **e**. **12 years**.**

Alternate Type:

Let Present age of B=x and present age of A=42-x

Then, 18 years ago A’s age=x and B’s age=x-(42+2x)=3x-42

By given condition, A’s present age=2×(B’ s age some years ago)

42-x=2(3x-42)

x=18

B’s present age=18 years and A’s present age=24 years**.**

8**. **A father says to his son, ‚7 years ago my age was 6 times of your age at that time & after 4 years my age will be four times of your age” Find the present age of the man?

**(a) **7

**(b) **7**. **2

**(c) **7**. **5

**(d) **8

**Answer: (c)**

**Explanation:**

Let us take son’s age as x, father’s age as y

7yrs ago, y-7= 6(x-7)

y-7= 6x-42

6x-y = 35 —-1

Y+4= 4(x+4)

4x-y= 12 —–2

Solve the two equations,

X= 7**. **5, y= 10

Son’s age is 7**. **5yrs

9. 10 years ago, the average age of family of 4 members was 26yrs**. **Two children have been born; the average age of the family is same today**. **The sum of the ages of the two children is?

**(a) **8yrs

**(b) **10yrs

**(c) **12yrs

**(d) **15yrs

**Answer: (c)**

**Explanation:**

Sum of ages of 4 members= 26×4= 104

Ten years ago, 104+(4×10)= 144yrs

Members in the family is now 4+2= 6

Sum of the ages of 6 members= 26×6= 156

= 12yrs

10**. **The average of a father and his two sons is 27 years**. **Five years ago, the average age of the two sons was 12 years**. **If the difference between the age of the two sons is 4 years, then the present age of the father is: [SSC Grad**. **2000]

**(a) ** 34 years

**(b) **47 years

**(c) **64 years

**(d) **27 years

**Answer: (b)**

**Explanation:**

Five years ago the average age of two sons =12 years

Their present average age = (12+5) = 17 years

Sum of their ages = 17 × 2 =34 years

Average age of three of them = 27 years

Sum of their ages = 27 × 3 =81 years

Father’s ages = 81 – 34 = 47 years