| Direction: In the following questions two quantities I and II are given. Solve both the quantities and choose the correct option accordingly. |
| I. The ratio of the age of Raj to that of Rajan 8 years ago is 3:4. 4 years hence, the ratio of the age of Raj to that of Rajan will become 10 : 12. What is the average age of both Raj and Raj an together? |
| II. My brother is 3 years older than me. My father was 27 when my sister was born while my mother was 26 when I born. If my sister was 3 years old when my brother born, then what was the age of my father when my brother was born? |
A) Quantity I > Quantity II
B) Quantity II > Quantity I
C) Quantity I > Quantity II
D) Quantity I < Quantity II
E) Quantity I = Quantity II or relation can't be established.
Correct Answer: B
Solution :
Quantity I. Let the ages of Raj and Rajan 8 yrs ago be 3x and 4x respectively. Raj's age 4 years hence \[=(3x+8)+4=(3x+12)\]years Raman's age 4 years hence \[=(4x+8)+4=(4x+12)\]years. Then, \[\frac{3x+12}{4x+12}=\frac{10}{12}\] \[\Rightarrow \]36x + 144 = 40x + 120 \[\therefore \] x = 6 Present age of Raj = 18 +8 =26 years Present age of Rajan =24 + 8 = 32 years \[\therefore \] Average age\[=\frac{26+32}{2}=\frac{58}{2}=29\]years Quantity II. My brother was horn 3 years after my sister was born. \[\therefore \] Father's age when my brother was born = (27 + 3) years = 30 years Thus, Quantity I < Quantity II
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