CAT Question of the Week - 82 Days to CAT 2015

Mr Sharma invested 10 lakh to buy shares in four companies–A, B, C and D. These companies belonged to the IT, real estate, pharmaceutical and banking sectors—not necessarily in that order. The amounts he spent to buy these shares were A - 1 lakh, B - 2 lakh, C - 3 lakh and D - 4 lakh. The returns he was expecting at the end of one year, from companies A, B, C and D were 10%, 20%, 40% and 30% respectively.
At the end of one year, a company in either the real estate or the software sector gave him double the expected returns, while a company in either the pharma or the banking sector gave one-and-a-half times the expected returns. The returns from the other two companies were as expected.

1. What is the maximum percentage returns that 
Mr Sharma would have earned at the end of the year? (A) 41% (B) 43% (C) 47% (D) 49%

2. The minimum percentage returns that Mr Sharma would have earned at the end of the year is (A) 37.5% (B) 35.6% (C) 30.2% (D) 32%

3. If the returns earned by 
Mr Sharma was 33.5%, then which of the following statements is true?
A) Company A belonged to the real estate or the software sector. 
B) Company B belonged to the real estate or the software sector. C) Company C belonged to the pharma or the banking sector.
D) Company D belonged to the pharma or the banking sector.

4. If it is known that company D gave one and a half times the expected returns, then which of the following could be the returns of Mr Sharma at the end of one year? (A) 45% (B) 40 % (C) 38% (D) 36%
Solutions:
1. The maximum percentage returns occur when the investments expected to earn maximum returns deliver more than expected returns.
= 0.10 + 0.40 + 2.40 + 1.80
= 4.7 lakh, i.e., 47%            Ans: Choice(C)

2. The minimum percentage returns are obtained when the companies expected to give the minimum returns gave more than the expected returns.
= 0.20 + 0.60 + 1.20 + 1.20
=3.20 lakh,  ie.32% 
Ans: Choice (D)

3. For Mr Sharma to get a return of 33.5%, which is very close to the least possible return he can get, the only possibility is that B belonged to either the real estate or the software sector and A belonged to either the pharma or the banking sector.     
Ans: Choice (B)

4. If company D gave one and half times the expected returns, his overall return could be
= 0.1 + 0.4 + 2.4 + 1.8 = 4.7 lakh = 47% or
= 0.1 + 0.8 + 1.2 + 1.8 = 3.9 lakh = 39% or= 0.2 + 2.4 + 1.2 + 1.8 = 3.6 lakh = 36%.  
Ans: Choice(D)