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The difference between the ages of a boss and his subordinate is 16 years. Four years ago, the respective ratio of the ages of the boss and the subordinate was 11:7 then, what is the present age of subordinate?
  • a)
    32 years
  • b)
    28 years
  • c)
    36 years
  • d)
    40 years
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
The difference between the ages of a boss and his subordinate is 16 ye...
Let the present age of the subordinate be x years
∴ Present age of the boss = (x + 16) years

⇒ 7x + 84= 11x - 44
⇒ 11x - 7x = 84 + 44
∴ x = 128/4 = 32 years
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Most Upvoted Answer
The difference between the ages of a boss and his subordinate is 16 ye...
Understanding the Problem
The problem states that the difference between the ages of a boss and his subordinate is 16 years. Additionally, four years ago, the ratio of their ages was 11:7.
Step 1: Setting Up Equations
Let:
- The current age of the subordinate be \( x \).
- The current age of the boss be \( x + 16 \).
Four years ago:
- The age of the subordinate was \( x - 4 \).
- The age of the boss was \( x + 16 - 4 = x + 12 \).
Given the ratio of their ages four years ago:
\[
\frac{x + 12}{x - 4} = \frac{11}{7}
\]
Step 2: Cross Multiplying
Cross multiply to eliminate the fraction:
\[
7(x + 12) = 11(x - 4)
\]
Expanding both sides:
\[
7x + 84 = 11x - 44
\]
Step 3: Solving for x
Rearranging the equation gives:
\[
84 + 44 = 11x - 7x
\]
\[
128 = 4x
\]
\[
x = 32
\]
Step 4: Conclusion
The current age of the subordinate is \( 32 \) years.
Final Answer
Thus, the present age of the subordinate is:
- Option A: 32 years.
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The difference between the ages of a boss and his subordinate is 16 years. Four years ago, the respective ratio of the ages of the boss and the subordinate was 11:7 then, what is the present age of subordinate?a)32 yearsb)28 yearsc)36 yearsd)40 yearsCorrect answer is option 'A'. Can you explain this answer?
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