Question

Which is better investment?
First: 16% Rs. 100 shares at 80 or
Second: 20% of Rs. 100 shares at 120?
A) First
B) Second
C) A and B
D) None of these

Answer 1

Hint: Given nominal and market values of 1 share in both the cases. Calculate the income using formula x% of Rs. Y. Calculate the income on Rs. 80 with 16%, Rs.1 in the first case and income on Rs. 120 with 20%, Rs.1 in second case. In both cases compare the income on Rs.1 and if the value in one case is greater than the other then it is a better investment.

Complete step-by-step answer:
First case: We are given that 16% of Rs. 100 shares at 80 means.
Market value of one share is 80 rupees. Nominal value of one share is 100 rupees.
We have to find the income generated on Rs. 80 when 16% of Rs. 100.
 $
  16\% ofRs.100 \\
   = \dfrac{{16}}{{100}} \times 100 \\
   = Rs.16 \\
  $
Income generated on Rs. 1 is
 $
   = \dfrac{{16}}{{80}} \\
   = \dfrac{1}{5} \\
   = Rs.0.20 \\
  $
Second case: We are given that 20% of Rs. 100 shares at 120 means.
Market value of one share is 120 rupees. Nominal value of one share is 100 rupees.
We have to find the income generated on Rs. 120 when 20% of Rs. 100.
 $
  20\% ofRs.100 \\
   = \dfrac{{20}}{{100}} \times 100 \\
   = Rs.20 \\
  $
Income generated on Rs. 1 is
 $
   = \dfrac{{20}}{{120}} \\
   = \dfrac{1}{6} \\
   = Rs.0.167 \\
  $
The income generated on 1 rupee when the nominal value is shared is greater in the first case.
Therefore, 16% Rs. 100 shares at 80 is a better investment.
So, the correct answer is “Option A”.

Note: Another approach to solve the above problem
First case:Another approach to solve the above problem
First case:
$
   \to P\% on 80 = 16\% on100 \\
   \to \dfrac{P}{{100}} \times 80 = \dfrac{{16}}{{100}} \times 100 \\
   \to P = \dfrac{{16 \times 100}}{{80}} \\
  P = 20\% \\
 $
Second case:
$
   \to P\% on 80 = 16\% on100 \\
   \to \dfrac{P}{{100}} \times 120 = \dfrac{{20}}{{100}} \times 100 \\
   \to P = \dfrac{{20 \times 100}}{{120}} \\
  P = 16.67\% \\
 $
Therefore, first investment is clearly better.