| Direction: In each of the following questions you have to find out that which of the following statement/statements is/are redundant for determining the answer of the given question or can be dispensed with. |
| What will be the sum of the ages of the father and the son after six years? |
| I. The father's present age is thrice the son's present age. |
| II. After eight years the ratio of the father's age to the son's age will become 17 : 7. |
| III. The difference between the father's age and the son's age is equal to the double of the son's age. |
A) Only I
B) Only either I or III
C) Any two of the three
D) Only III
E) Only I or II
Correct Answer: B
Solution :
From I. Father's age = 3 \[\times \] Son's age ...(i) From II. \[\frac{F+8}{S+8}=\frac{17}{7}\] \[\Rightarrow \] 7F+ 56 = 17S + 136 ... (ii) From I and II. \[7\times 3S+56=17S+136\] \[\Rightarrow \]\[215-17S=136-56=80\] \[\Rightarrow \]\[4S=80\] \[\therefore \]\[S=20\,years\] \[\therefore \] Reqd sum = 20 + 6 + 3 \[\times \]20 + 6 = 26 + 66 = 92 years From III. Father's present age = F - S = 2S \[\Rightarrow \]\[F=3S\] From II and III. We can also find the sum of ages of father and son after six years. Hence either I or III can be dispensed with.
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