# Aptitude - Problems on Ages - Discussion

Discussion Forum : Problems on Ages - Data Sufficiency 2 (Q.No. 1)
Directions to Solve

Each of the questions given below consists of a question followed by three statements. You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the question.

1.
 What is Arun's present age? I. Five years ago, Arun's age was double that of his son's age at that time. II. Present ages of Arun and his son are in the ratio of 11 : 6 respectively. III. Five years hence, the respective ratio of Arun's age and his son's age will become 12 : 7.
Only I and II
Only II and III
Only I and III
Any two of the three
None of these
Explanation:

II. Let the present ages of Arun and his son be 11x and 6x years respectively.

I. 5 years ago, Arun's age = 2 x His son's age.

 III. 5 years hence, Arun's Age = 12 Son's age 7

Clearly, any two of the above will give Arun's present age.

Discussion:
28 comments Page 1 of 3.

Aiswarya said:   3 years ago
5 years hence means after 5 years.

Am I right?
(7)

BhumikaNegi said:   3 years ago
1 and 2 is also valid because.

From 1 we get : x - 5 = 2x i.e x= x-5/2.
From 2 we get : 12x + 5 = 7x + 5.
By putting 1 in 2 , we get 12(x-5/2) + 5 = 7(x-5/2)+5,
i.e 12x - 50 = 7x -25.
x = 5.
(2)

Prott said:   4 years ago
All the 3 options are correct in case of Arun's present age being 55 and his Son's present age being 30.

(i) 5y ago, Arun was at 50, his son's was at 25- satisfying the condition.
(ii) At present, 55:30=11:6, satisfies the condition again.
(iii) 5y hence, Arun will be 60, his son will be 35 (the ratio is 60:35=12:7)- satisfies the condition as well.
(4)

Bangari potla said:   4 years ago
Thanks all for explaining the answer.
(1)

Bangari potla said:   4 years ago
What is the meaning of five years hence? Please tell me.

Shubham said:   4 years ago
Present year ratio 11x/6x.
Five years hence ratio will 12x/7x.

So,
11x+5 / 6x+5 = 12/7.
So, 77x+35= 72x+50.
5x=25.
X=5.

Even from statements 2 and 3 we can get answer.
(1)

Simna said:   4 years ago
How can Statement 2 & Statement 3 help solve the problem. His age = 2*Sons is a must statement. Therefore how can this statement be true "Any two of the three".
(2)

Praveen said:   7 years ago
@Latha Bv.

By Statement I :
Let x be Arun's present age, s be son's present age
x-5 = 2(s-5),
x-5 = 2s-10,
x = 2s-5.

By Statement III :
x+5/ s+5 = 12/7

Substituting eqn of x from Statement I.

2s-5+5/s+5 = 12/7

2s/ s+5 = 12/7

7(2s) = 12(s+5)
14s - 12s = 60
2s = 60
s = 30(Son's Present Age).

Now, substitute the value of s in the eqn of x (Statement I).
x = 2s-5
= 2(30)-5
= 60-5
x = 55(Arun's Present Age).

Thus Arun's Present Age can be found from Statement I and III too.

Thus Option D(Any two of three) is correct.
(3)

Latha BV said:   8 years ago
The present age of Arun = 11x.
The present age of Arun's son = 6x.

I) 5 years ago Arun's age was double of his son's age that means (11x - 5) = 2 (6x - 5).
11x - 5 = 12x - 10.
12x - 10 - 11x + 5 = 0.
x = 5.

2) Statement 2 is already used in statement 1 to get the value of x.

3) Five years hence the respective ratio of Arun's age and his son's age will become 12 : 7 that means.

11x + 5/6x + 5 = 12/7.

7 (11x + 5) = 12 (6x + 5).
77x + 35 = 72x + 60.
x = 5.
Arun's present age = 11x.
= 11 * 5.
= 55.

So from the statement 1 and 2, we get the value of x is 5.

And from the statement 2 and 3 we get the value of x is also 5.

At last, we get the present age of Arun is 55, and here the most used statement was 2 hence we use only 1 and 2 are else 2 and 3 but not by 1 and 3, therefore, the answer should be E but not D.
(1)

Asiri said:   8 years ago