Comprehension
Shabnam is considering three alternatives to invest her surplus cash for a week. She wishes to guarantee maximum returns on her investment. She has three options, each of which can be utilized fully or partially in conjunction with others.
Option A: Invest in a public sector bank. It promises a return of +0.10%.
Option B: Invest in mutual funds of ABC Ltd. A rise in the stock market will result in a return of +5% while a fall will entail a return of −3%.
Option C: Invest in mutual funds of CBA Ltd. A rise in the stock market will result in a return of −2.5% while a fall will entail a return of +2%.
Question: 1

The maximum guaranteed return to Shabnam is

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Her return depends on whether the market rises or falls, so the guaranteed return is the smaller of the two. Find the mix of B and C that makes the two returns equal.
Updated On: Nov 4, 2026
  • 0.25%
  • 0.20%
  • 0.10%
  • 0.15%
  • 0.30%
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The Correct Option is B

Solution and Explanation

Step 1: Express the returns:
Let the fractions invested in A, B, C be \(a, b, c\) with \(a+b+c=1\). If the market rises, the return (in %) is \(R=0.1a+5b-2.5c\). If it falls, the return is \(F=0.1a-3b+2c\). The guaranteed return is \(\min(R,F)\), which we want to maximise.

Step 2: Best mix of B and C alone:
Put fraction \(y\) in B and \(1-y\) in C. Then \(R=5y-2.5(1-y)=7.5y-2.5\) and \(F=-3y+2(1-y)=2-5y\). \(R\) rises with \(y\) and \(F\) falls with \(y\), so the minimum is largest when they are equal: \(7.5y-2.5=2-5y\Rightarrow y=0.36\). The guaranteed return is then \(7.5(0.36)-2.5=0.2\%\).

Step 3: Does adding A help?
If a fraction \(a\) is put in A (return 0.1% in both cases), the rest \(1-a\) can guarantee at most 0.2% per unit invested. So the guaranteed return is at most \(0.1a+0.2(1-a)=0.2-0.1a\), which is largest at \(a=0\). So A should not be used.

Step 4: Conclusion:
The maximum guaranteed return is \(0.20\%\), obtained with 36% in B and 64% in C.

Final Answer:
The correct option is (2): 0.20%.
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Question: 2

What strategy will maximize the guaranteed return to Shabnam?

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Work out the return in the “rise” case and the “fall” case for each option; the best strategy is the one whose worse case is largest.
Updated On: Nov 4, 2026
  • 100% in option A
  • 30% in option A, 32% in option B and 38% in option C
  • 64% in option B and 36% in option C
  • 1/3 in each of the three options
  • 36% in option B and 64% in option C
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The Correct Option is

Solution and Explanation

Step 1: Returns in the two cases:
For fractions \(a,b,c\) in A, B, C: rise return \(R=0.1a+5b-2.5c\) and fall return \(F=0.1a-3b+2c\) (in %). The guaranteed return is \(\min(R,F)\).

Step 2: Evaluate each option:
(1) 100% in A: \(R=F=0.1\). Guaranteed 0.1%.
(5) 36% B, 64% C: \(R=1.8-1.6=0.2\), \(F=-1.08+1.28=0.2\). Guaranteed 0.2%.
(3) 64% B, 36% C: \(R=3.2-0.9=2.3\), \(F=-1.92+0.72=-1.2\). Guaranteed \(-1.2\%\).
(4) one third each: \(R\approx0.867\), \(F=-0.3\). Guaranteed \(-0.3\%\).
(2) 30% A, 32% B, 38% C: \(R=0.03+1.6-0.95=0.68\), \(F=0.03-0.96+0.76=-0.17\). Guaranteed \(-0.17\%\).

Step 3: Compare:
The largest guaranteed return is 0.2%, from option (5). This is also the maximum possible (see the previous question), so option (5) is the best strategy.

Final Answer:
The correct option is (5): 36% in option B and 64% in option C.
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