Aptitude - Problems on Ages - Discussion

Discussion :: Problems on Ages - Data Sufficiency 2 (Q.No.1)

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.

 [A]. Only I and II [B]. Only II and III [C]. Only I and III [D]. Any two of the three [E]. 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.

 Surbhi said: (Jan 17, 2011) What's the meaning of five years hence?

 Anshu said: (Jun 10, 2011) Please tell meaning of five year hence.

 Mahendra said: (Jul 1, 2011) What is this question I didn't get the question itself, so kindly explain me please.

 Hema said: (Jul 12, 2011) Please explain briefly.

 Poornima said: (Aug 8, 2011) Can someone explain this?

 Harsha said: (Aug 10, 2011) 5 years hence means- after 5 years.

 Garv said: (Sep 25, 2011) Answer can be non of these Five year ago son's age-x arun's age-2x present age (x+5)11=(2x+5)6 x=25 then present 30 after 5 year son age 35 arun 60 Condition satisfied.

 Siddu said: (Jan 3, 2012) Present : 11x, 6x 5 years ago 11(x-5), 6(x-5)= 11(x-5)= 2(6(x-5)) 11x-55= 2(6x-30) x=5

 Akash said: (Feb 18, 2012) How statement 3 is true? I can't get solution for 3rd statement.

 Aiswarya said: (Jul 19, 2013) Easy way to catch up this problem: Present age be x. Ratio given 11:6 so present age ratio is 11x:6x. Given that 5 years ago so we 11(x-5) = 6(x-5). Aruns age is twice of his sons age :11(x-5) = 2(6(x-5)). Hence x = 5.

 Amal said: (Sep 5, 2014) All the statements are true. But there is a logic. What dose "only "means? I think the answer is "E".

 Datta said: (Mar 5, 2015) 11:6, so 11x:6x. 5 years ago 11(x-5) = 6(x-5). 11(x-5) = 2(6(x-5)). Hence x = 5.

 Gopi Krishna Arava said: (Mar 27, 2015) X value is ok. But how can it satisfied both I and II rule?

 Kuzne4Ik said: (Jul 20, 2015) 1. x = 11/6*y. 11/6*y = 12/7*y+5. y = 42(son). x = 77(father). 2. x = 2*y-5. x = 11/6*y. 2*y-5=11/6*y. y = 30 (son). x = 55(father). 3. x = 2*y-5. x = 12/7*y+5. 2*y-5 = 12/7*y+5. y = 35(son). x = 65(father). Because of different results, only 2 from 3 can be satisfied.

 Raghavendra said: (Sep 10, 2015) There are two unknowns and requires no more than 2 equations to determine all unknowns! No need to calculate anything!

 Nish said: (Sep 10, 2015) Condition 1 and 2, 1 and 3 are enough. But 2 and 3 are note sufficient. Hence answer cannot be any two of above.

 Chetan said: (Oct 16, 2015) For son's present age = 30 and father's present age = 55 all the conditions satisfy.

 Chetan said: (Oct 18, 2015) For son's present age = 30 and father's present age = 55 all the conditions satisfy.

 Asiri said: (Feb 4, 2016) Answer should be E. You can get an answer by joining 1, 2 & 2, 3 but not by 1, 3. Therefore D (Any two of the three) is wrong.

 Latha Bv said: (Sep 9, 2016) 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.

 Praveen said: (Apr 13, 2017) @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.

 Simna said: (Mar 26, 2020) 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".

 Shubham said: (May 8, 2020) Simna here is your answer. 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.

 Bangari Potla said: (May 27, 2020) What is the meaning of five years hence? Please tell me.

 Bangari Potla said: (May 27, 2020) Thanks all for explaining the answer.

 Prott said: (Nov 22, 2020) 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.

 Bhumikanegi said: (Mar 17, 2021) 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.

 Aiswarya said: (Jun 10, 2021) 5 years hence means after 5 years. Am I right?