Direction: In each of the following questions, a question is asked followed by three statements. You have to study the questions and all the three statements given and decide whether any information provided in the statement(s) is/are redundant and can be dispensed with while answering the questions.
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What will be the sum of the ages of father and the son after five years?
A. Father’s present age is twice son’s present age.
B. After ten years the ratio of father’s age to the son’s age will become 12 : 7.
C. Five years ago the difference between the father’s age and son’s age was equal to the son’s present age.
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- A or B only
- B or C only
- A or C only
- C only
- A or B or C only
Correct Option: E
On the basis of above given details in question ,
Let father’s present age is F and son’s present age is S .
From statement A , Father’s present age = 2 x son’s present age
⇒ F = 2S
From statement B , After 10 years , ratio of father’s age to the son’s age = 12 : 7
⇒ ( F + 10 ) : ( S + 10 ) = 12 : 7
From statement C , 5 years ago , father’s age - son’s age = son’s present age
⇒ ( F - 5 ) - ( S - 5 ) = S
From statement B and A , we have
⇒ ( 2S + 10 ) / ( S + 10 ) = 12 / 7 { ∴ putting F = 2S }
⇒ 14S + 70 = 12S + 120 ⇒ 14S - 12S = 120 - 70 ⇒ 2S = 50 ⇒ S = 50 / 2 = 25 years and F = 2 x 25 = 50 years
After 5 years , Father’s age = Father’s present age + 5 = 50 + 5 = 55 years
and Son’s age = Son’s present age + 5 = 25 + 5 = 30 years
Sum of the ages of father and the son after five years = 55 + 30 = 85 years
Any two of the three statements are sufficient to answer the question (As to find the two unknowns we need two equations). Hence, anyone of the statements can be dispensed with.
