Stocks & Shares Questions and Answers

Answer: C

Find how many shares Rs. 4455 buys at Rs. 8.25 each.

\[ n = \frac{4455}{8.25} = 540 \text{ shares} \]

Each Rs. 10 share pays a 12% dividend:

\[ 0.12 \times 10 = \text{Rs. } 1.20 \text{ per share} \]

\[ 540 \times 1.20 = \text{Rs. } 648 \]

The dividend rides on the Rs. 10 face value, not on the Rs. 8.25 paid.

Answer: B

Correct answer: 12%

Rs. 125 buys Rs. 100 of stock, which pays Rs. 15 a year.

\[\text{Yield} = \frac{15}{125} \times 100 = 12\%\]

Buying above par lowers the effective return below the nominal 15%, which is the mirror image of buying at a discount.

Answer: D

For an investment of Rs.80, income = Rs.10
For an investment of Rs.100, income = Rs. (100 * 10)/80 = Rs.12.5
For an investment of Rs.70, income = Rs.15
For an investment of Rs.100, income = Rs. (100 * 15)/70 = Rs.21.43
For an investment of Rs.75, income = Rs.12
For an investment of Rs.100, income = Rs. (100 * 12)/75 = Rs.16

Answer: B

In stock problems, a "\( r\% \) stock at \( m \)" means Rs. 100 of face value costs Rs. \( m \) and pays Rs. \( r \) a year, so the yield on money invested is \( \tfrac{r}{m} \).

\[ \text{9\% at 75 yields } \frac{9}{75} = 12\%, \qquad \text{10\% at 80 yields } \frac{10}{80} = 12.5\% \]

Equal incomes from the two parts:

\[ 0.12x = 0.125(9800 - x) \]

\[ 0.12x = 1225 - 0.125x \quad\Longrightarrow\quad 0.245x = 1225 \]

\[ x = \text{Rs. } 5000 \]

Each part then yields Rs. 600.

Answer: C

FUZZTONE has eight letters with Z appearing twice: vowels U, O, E and consonants F, Z, Z, T, N.

Treat the three vowels as one block, giving six units among which Z repeats:

\[ \frac{6!}{2!} = 360 \]

Within the block the three distinct vowels arrange in

\[ 3! = 6 \text{ ways} \]

\[ 360 \times 6 = 2160 \]

The repeated Z is divided out among the units, but the vowels are all different so no division is needed inside the block.

Answer: B

In stock problems, a "\( r\% \) stock at \( m \)" means Rs. 100 of face value costs Rs. \( m \) and pays Rs. \( r \) a year, so the yield on money invested is \( \tfrac{r}{m} \).

\[ \text{yield} = \frac{16}{64} = 25\% \]

\[ \text{investment} = \frac{1500}{0.25} = \text{Rs. } 6000 \]

Equivalently, every Rs. 64 invested returns Rs. 16, so \( 1500 \times \tfrac{64}{16} = 6000 \).

Answer: B

Correct answer: Rs. 225

Each Rs. 100 of stock costs Rs. 120 and pays Rs. 9.

\[\text{Stock bought} = \frac{3000}{120} \times 100 = \text{Rs. } 2500 \text{ face value}\]

\[\text{Income} = \frac{9}{100} \times 2500 = \text{Rs. } 225\]

The dividend is always reckoned on the face value, never on the price paid.

Answer: B

Correct answer: Rs. 20

The dividend is reckoned on the face value.

\[\text{Dividend per share} = \frac{8}{100} \times 25 = \text{Rs. } 2\]

For that Rs. 2 to represent a 10% return, the price paid must be

\[\frac{2}{10} \times 100 = \text{Rs. } 20\]

He must therefore buy below par, which is what raises his yield above the nominal 8%.

Answer: C

Brokerage is added to the market price when buying.

\[ \text{cost per share} = 20 + 2.5\% \text{ of } 20 = 20 + 0.50 = \text{Rs. } 20.50 \]

\[ n = \frac{8200}{20.50} = 400 \]

Ignoring the brokerage would give 410 - exactly the adjacent option.

Answer: D

In stock problems, a "\( r\% \) stock at \( m \)" means Rs. 100 of face value costs Rs. \( m \) and pays Rs. \( r \) a year, so the yield on money invested is \( \tfrac{r}{m} \).

\[ \text{9\% at 96 yields } \frac{9}{96} = \frac{3}{32}, \qquad \text{12\% at 120 yields } \frac{12}{120} = \frac{1}{10} \]

Equal dividends:

\[ x \times \frac{3}{32} = y \times \frac{1}{10} \quad\Longrightarrow\quad \frac{x}{y} = \frac{32}{30} = \frac{16}{15} \]

The investments are in the inverse ratio of the yields, so the lower-yielding stock takes the larger sum.