__DATA SUFFICIENCY
Questions – Problems on Ages__

a)If the data in statement I alone are sufficient to answer the
question, while the data in statement II alone are not sufficient to answer the
question.

b)If the data in statement II alone are sufficient to answer the
question, while the data in statement I alone are not sufficient to answer the
question.

c)If the data in both
the statement I and II together are necessary to answer the question.

d)If the data in either statement I alone or statement II alone are
sufficient to answer the question.

e)If the data in both the statement I and II are not sufficient to
answer the question.

1.What is the present age of Parimala?

1. Parimala is 5
times younger than Rajini

2. The sum of the
ages of Supriya and Rajani is 80 years Supriya’s age is thrice the age of Rajani

**Answer : C**

**Explanation: **

__Statement 1 alone:__

Parimala
is 5 times younger than Rajani

Parimala = 1/5 x Rajani

Statement 1 alone is not sufficient to answer the question

__Statement 2 alone :__

Supriya + Rajani = 80 years

Supriya
= 3 x Rajani

= > Supriya: Rajani – 3: 1

Age of Rajani = 80 x ¼ = 20

Statement 2 alone is not sufficient to answer
the question

__Both statements together:__

Age of Rajani is 20 years

Parimala
= 1/5 x Rajini

= > Parimala = 20 x 1/5 = 4 years

Hence,
both the statements I and II together are necessary to answer the question.

2.What
is the present age of the mother?

1. The
present age of mother and son are in the ratio of 4:1, respectively.

2. 20
years hence the ratio of the ages of mother and son will be 16:9, respectively.

**Answer: C**

**Explanation :**

__ ____Statement 1 alone :__

The ratio of the ages of mother and son is 4:1

From this, we can't
find the age of the mother

So statement 1
alone is not sufficient to answer the question

__Statement 2 alone :__

After 20 years, the ages of mother and son
will be in the ratio of 16: 9 respectively

The statement
alone is not sufficient to answer the question

Both statements 1
and 3 together :

Let the present
ages of mother and son are 4x and x respectively

After 20 years
=> Mother /Son = 4x + 20/x +20 = 16/9

=
>36x +180 = 16x +320

= > 20x =140

= > x=7

The age of the
mother is 4x 7 = 28 years

So both
statements together are needed to answer the question

3.What
is the age of Divya after 8 years?

1.Divya is 3 times elder than Bhavya

2.Surya’s
age is thrice the age of Bhavya

**Answer: E**

**Explanation :**

__Statement
1 alone : __

Divya = 3 x Bhavya

__Statement
2 alone:__

Surya = 3 x Bhavya

__Both
statement together :__

Divya = Surya = 3 Bhavya

The age of Divya
cannot be found

Both the
statement together are not sufficient to answer the question.

4.What
was the age of Srimanth 6 years ago?

1.The
ratio between the ages of Srimanth and Sameer is 7:5 respectively

2.Srimanth
is 8 years elder than Sameer

**Answer: C**

**Explanation:**

__Statement 1 alone :__

Srimanth : Sameer = 7:5

__Statement 2 alone:__

Srimanth – Sameer = 8 years

__Both
statement 1 and 2 together :__

Let the ages of Srimanth and Sameer be 7x
and 5x respectively

Srimanth – Sameer => 7x
-5x = 8 years => x = 4 years

So the present age of Sameer is (7 x 4) =
28 years

6 years ago, the age of Srimanth was =>
28-6 = 22 years

Hence, data in both the statements I
and II together are necessary to answer the question.

5.What is the present of Prasad?

1.Prasad is 8 years younger than Sahithi

2.The ratio between the ages of Prasad and Madhuri is 5:8 respectively

**Answer : E**

**Explanation :**

__Statement 1 alone :__

Prasad =Sahithi + 8 years

__Statement 2 alone:__

Prasad: Madhuri = 5 : 8

__Both statements together :__

Prasad = Sahithi + 8 years

Prasad : Madhuri = 5 :8

We cannot find the age of Prasad using both statements together

6.What was the age of the mother, when her youngest daughter was
born?

1.The present age of the mother is 36 years

2.The mother's age is 3/2 times the sum of the ages of her two
daughters born at intervals of 4 years

**Answer: A**

**Explanation
:**

__Statement 1 alone :__

Mother’s present age = 36

Statement
1 alone is not sufficient

__Statement 2 alone :__

Let the age of the youngest daughter
be x. Then the age of another daughter will be (x + 4)

Mother’s
age = 3/2 ( (x+ (x+4))

Statement
2 alone is not sufficient

__Both statements together :__

Mother’s present age = 3/2 ( x +(x+4)

= > 36 = 3/2 (2x+4)

= > 2x+ 4 = 24

=>x = 10 years

The age of the mother
when the younger daughter was born =>36-10 = 26 years

Both statements together are
sufficient to answer the question

7.What is the present age of Murty?

1.After 48 years, the age of Murty will be 3 times his present
age

2.14 years ago, Murty celebrated his 10^{th} birthday

**Answer
: D**

**Explanation
:**

__Statement 1 alone :__

Let the present age of Murty be x.

x + 48 = 3x => 2x = 48 => x = 24

So
statement 1 alone is sufficient to answer the question

__Statement 2 alone :__

14 years ago, Murty celebrated his 10^{th}
birthday

So 14 years year , his age was 10 years => Murty’s
present age = 14 + 10 = 24 years

Statement
2 alone is sufficient to answer the question

Therefore, either statement 1 alone or
statement 2 alone is sufficient to answer the question

8.How old each of Ramesh and Suresh?

1.6
years ago,
Ramesh was 3 times elder than Suresh

2.After 8 years, Ramesh
will be twice as old as Suresh will be

__Answer : C__

__Explanation: __

__Statement 1 alone :__

6 years ago, the ratio of Ramesh and
Suresh = 3:1

Statement
1 alone is not sufficient to get the answer

__Statement 2 alone :__

8 years hence, the ratio of Ramesh and
Suresh will be 2:1

Statement
2 alone is not sufficient to get the answer

__Statements 1 and 2 together :__

Let the age of Ramesh and Suresh 6
years ago be 3x and x respectively

After 8 years => Ramesh/Suresh =(
3x + 6+ 8)/(x +6 +8) = 2/1

=
>(3x + 14)/ (x + 14) = 2/1

=
>(3x + 14) = (2x + 28)

=
>x= 14

Present age of Ramesh and Suresh are => (3x + 6) and
(x+6) respectively

=>
48 and 20 years respectively

So data given in both statements together are sufficient

9.Two siblings have some peculiarities
about their ages. What are their present ages?

1.Their present ages are odd integers

2.The sum of their ages is 15 years

**Answer: C**

**Explanation :**

__Statement 1 alone :__

The
present ages of two siblings are odd integers

Many
possibilities are there

Statement
1 alone is not sufficient to answer the question

__Statement 2 alone:__

The
sum of their ages is 15 years

The
possibilities are (14,1),(13,2),(12,3),(11,4),(10,5), (9,6) and (8,7)

We
have more than one possible answer

So
statement 2 alone is not sufficient to answer the question

__Combining both statements :__

The
Sum of their present ages is 15 years and their ages are odd integers

We
can get only one combination i.e (13,2)

Then
their ages are 13 years and 2 years.

Both
statements together are sufficient to answer the question.

10.Three brothers A, B, and C are of
different ages. What is the age of C 5
years ago?

1.A is 4 years elder than B

2.The sum of the ages of B and C is 19
years and the product of their ages is 88 years

**Answer
: B**

**Explanation:**

__Statement 1 alone :__

The difference between the ages of A and B is given.

But we don’t have any information about C

So statement 1 alone is not sufficient to answer the
question

__Statement 2 alone:__

The sum of the ages of B and C is 19 => B+C = 19

Product of the ages of B and C is => BC = 88

(B-C)^{2}
= (B+C)^{2} -4BC

=
>(B-C)^{2} = 19^{2} -
(4 x 88)

=
>(B-C)^{2}= 361-352

=
>(B-C)^{2}= 9

=>(B-C)=
3

On solving , B = 11 and C= 8

Therefore, the age of C 5
years ago was (8-5) = 5 years

Statement
2 alone is sufficient to answer the question