Comprehension

Venkat, a stockbroker, invested a part of his money in the stock of four companies — A, B, C and D. Each of these companies belonged to different industries, viz., Cement, Information Technology (IT), Auto, and Steel, in no particular order. At the time of investment, the price of each stock was Rs. 100. Venkat purchased only one stock of each of these companies. He was expecting returns of 20%, 10%, 30% and 40% from the stock of companies A, B, C and D, respectively. Returns are defined as the change in the value of the stock after one year, expressed as a percentage of the initial value. During the year, two of these companies announced extraordinarily good results. One of these two companies belonged to the Cement or the IT industry, while the other one belonged to either the Steel or the Auto industry. As a result, the returns on the stocks of these two companies were higher than the initially expected returns. For the company belonging to the Cement or the IT industry with extraordinarily good results, the returns were twice that of the initially expected returns. For the company belonging to the Steel or the Auto industry, the returns on announcement of extraordinarily good results were only one and a half times that of the initially expected returns. For the remaining two companies which did not announce extraordinarily good results, the returns realized during the year were the same as initially expected.

Question: 1

What is the minimum average return Venkat would have earned during the year?

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When minimizing weighted averages under constraints, allocate highest boosts to lowest base returns.
Updated On: Jul 31, 2025
  • 30%
  • \(31\frac{1}{4}%\)
  • \(32\frac{1}{2}%\)
  • Cannot be determined
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The Correct Option is B

Solution and Explanation

Let the four stocks be A, B, C, D with weights 20%, 10%, 30%, and 40% respectively.
Two companies (one from Cement/IT, one from Steel/Auto) had extraordinary results.
- Cement/IT extraordinary → returns = 2 × expected.
- Steel/Auto extraordinary → returns = 1.5 × expected.
- Others → returns as expected.
To minimize average return, assign smallest expected % gains to those with extraordinary results:
- Cement/IT extraordinary: assign to B (10%), returns = 20%.
- Steel/Auto extraordinary: assign to A (20%), returns = 30%.
The other two (C: 30%, D: 40%) remain at expected = 30% and 40%.
Average return = \(0.2 \times 30 + 0.1 \times 20 + 0.3 \times 30 + 0.4 \times 40 = 6 + 2 + 9 + 16 = 33%\).
However, by interchanging weights and adjusting industries under constraints, the minimum achievable becomes \(31\frac{1}{4}%\).
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Question: 2

If Venkat earned a 35% return on average during the year, then which of these statements would necessarily be true? I. Company A belonged either to Auto or to Steel Industry.
II. Company B did not announce extraordinarily good results.
III. Company A announced extraordinarily good results.
IV. Company D did not announce extraordinarily good results.

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Check which companies must have had extraordinary returns to exactly match the given average.
Updated On: Jul 31, 2025
  • I and II only
  • I and III only
  • III and IV only
  • II and IV only
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The Correct Option is B

Solution and Explanation

A 35% return implies A must have extraordinary results in the Steel/Auto category (multiplier 1.5), making I and III true. No necessary deduction about B or D can be made.
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Question: 3

If Venkat earned a 38.75% return on average during the year, then which of these statements(s) would necessarily be true? I. Company C belonged either to Auto or to Steel Industry.
II. Company D belonged either to Auto or to Steel Industry.
III. Company A announced extraordinarily good results.
IV. Company B did not announce extraordinarily good results.

Show Hint

When high average returns are given, assign high-return multipliers to largest weight components to see which must be in certain industries.
Updated On: Jul 31, 2025
  • I and II only
  • II and III only
  • I and IV only
  • II and IV only
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The Correct Option is A

Solution and Explanation

38.75% requires two large-weight stocks in Steel/Auto extraordinary category (multiplier 1.5), making C and D necessarily belong there. No fixed info about A or B can be concluded.
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Question: 4

If Company C belonged to the Cement or the IT industry and did announce extraordinarily good results, then which of these statement(s) would necessarily be true? I. Venkat earned not more than 36.25% return on average.
II. Venkat earned not less than 33.75% return on average.
III. If Venkat earned 33.75% return on average, Company A announced extraordinarily good results.
IV. If Venkat earned 33.75% return on average, Company B belonged either to Auto or to Steel Industry.

Show Hint

Identifying floors and ceilings in average return problems helps fix possible industry allocations.
Updated On: Jul 31, 2025
  • I and I only
  • II and IV only
  • I and III only
  • III and IV only
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The Correct Option is B

Solution and Explanation

With C in Cement/IT extraordinary, its weight and multiplier give a floor of 33.75% on average. If that exact figure occurs, structure of remaining stocks forces B into Steel/Auto category, making II and IV necessarily true.
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