Aptitude - Problems on Ages

Each of the questions given below consists of a statement and / or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is / are sufficient to answer the given question. Read the both statements and

  • Give answer (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.
  • Give answer (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.
  • Give answer (C) if the data either in Statement I or in Statement II alone are sufficient to answer the question.
  • Give answer (D) if the data even in both Statements I and II together are not sufficient to answer the question.
  • Give answer(E) if the data in both Statements I and II together are necessary to answer the question.
1. 

What is Sonia's present age?

I. 

Sonia's present age is five times Deepak's present age.

 II. 

Five years ago her age was twenty-five times Deepak's age at that time.

A. I alone sufficient while II alone not sufficient to answer
B. II alone sufficient while I alone not sufficient to answer
C. Either I or II alone sufficient to answer
D. Both I and II are not sufficient to answer
E. Both I and II are necessary to answer

Answer: Option E

Explanation:

 I. S = 5D    D = S ....(i)
5

II. S - 5 = 25 (D - 5)    S = 25D - 120 ....(ii)

Using (i) in (ii), we get S = 25 x S - 120
5

4S = 120.

S = 30.

Thus, I and II both together give the answer. So, correct answer is (E).


2. 

Average age of employees working in a department is 30 years. In the next year, ten workers will retire. What will be the average age in the next year?

I. 

Retirement age is 60 years.

 II. 

There are 50 employees in the department.

A. I alone sufficient while II alone not sufficient to answer
B. II alone sufficient while I alone not sufficient to answer
C. Either I or II alone sufficient to answer
D. Both I and II are not sufficient to answer
E. Both I and II are necessary to answer

Answer: Option E

Explanation:

 I. Retirement age is 60 years.

II. There are 50 employees in the department.

Average age of 50 employees = 30 years.

Total age of 50 employees = (50 x 30) years = 1500 years.

Number of employees next year = 40.

Total age of 40 employees next year (1500 + 40 - 60 x 10) = 940.

Average age next year = 940 years = 23 1 years.
40 2

Thus, I and II together give the answer. So, correct answer is (E).


3. 

Divya is twice as old as Shruti. What is the difference in their ages?

I. 

Five years hence, the ratio of their ages would be 9 : 5.

 II. 

Ten years back, the ratio of their ages was 3 : 1.

A. I alone sufficient while II alone not sufficient to answer
B. II alone sufficient while I alone not sufficient to answer
C. Either I or II alone sufficient to answer
D. Both I and II are not sufficient to answer
E. Both I and II are necessary to answer

Answer: Option C

Explanation:

Let Divya's present age be D years and Shruti's present age b S years

Then, D = 2 x S       D - 2S = 0 ....(i)

 I. D + 5 = 9 ....(ii)
S + 5 5

II. D - 10 = 3 ....(iii)
S - 10 1

From (ii), we get : 5D + 25 = 9S + 45       5D - 9S = 20 ....(iv)

From (iii), we get : D - 10 = 3S - 30       D - 3S = -20 ....(v)

Thus, from (i) and (ii), we get the answer.

Also, from (i) and (iii), we get the answer.

I alone as well as II alone give the answer. Hence, the correct answer is (C).