Question

Adam's savings are equal to Ben's expenditure, which in turn is equal to Mary's savings. If Mary's savings are Rupees 50,000 and the incomes of Adam, Ben, and Mary are in the ratio 3:1:4, Mary's expenditure is less than thrice of Adam's expenditure and twice of Adam's expenditure is less than two times Ben's income, then which of the following could be true about Ben's income (\(I_B\))?

• A. \(18000<I_B<22000\)
• B. \(20000<I_B<25000\)
• C. \(23000<I_B<28000\)
• D. Data Inconsistent

Hint:

In complex word problems with multiple variables, the key is to define a single variable (like a common ratio 'x') and express all other quantities in terms of it. This simplifies the problem into solving inequalities for that single variable.

Answer 1

The Correct Option is B

Step 1: From the two given conditions, \(x\) is restricted to lie strictly inside \(20{,}000 < x < 25{,}000\) (call this the valid interval \(V\)).
Step 2: Check each option as an interval against \(V\) by comparing endpoints directly rather than testing a single number: option A's interval \((18{,}000,\,22{,}000)\) sticks out below \(V\)'s left edge, so part of it lies outside \(V\); option C's interval \((23{,}000,\,28{,}000)\) sticks out past \(V\)'s right edge, so part of it lies outside \(V\) too.
Step 3: Option B's interval \((20{,}000,\,25{,}000)\) matches \(V\) exactly, so it is the interval that could be true without any part falling outside the valid zone.
\[ \boxed{20{,}000 < I_B < 25{,}000} \]
Final Answer: Option (B).