A man has choice to invest in $₹ 100$ shares of two companies X and Y. Shares of company X are available at a premium of $20 %$ and it pays $5 %$ dividend whereas shares of company Y are available at a discount of $10 %$ and it pays $7 %$ dividend. If the man invests equally in both the companies and the sum of the returns from them is $₹ 1290$ , then find how much in all does he invest?

$₹ 20000$

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$₹ 21000$

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$₹ 21500$

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$₹ 21600$

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Solution

The correct option is D
$₹ 21600$

Step 1: Given data
Face value of Company X, $F_{x} = ₹ 100$
Premium% on Company X's shares, $P_{x} = 20 %$
Dividend% of Company X's shares, $D_{x} = 5 %$
Face value of Company Y, $F_{y} = ₹ 100$
Dividend% of Company Y's shares, $D_{y} = 7 %$
Discount% on Company Y's shares, $d_{y} = 10 %$
Sum of annual incomes of Company X and Company Y, $S = ₹ 1290$
Step 2: Calculate the annual income of Company X
As shares of Company X are at a premium of $20 %$
∴ $M a r k e t v a l u e, M_{x} = F a c e v a l u e + P r e m i u m % o f F a c e v a l u e = F_{x} + P_{x} % o f F_{x}$
$M_{x} = 100 + \frac{20}{100} \times 100 = 100 + 20 = ₹ 120$
It is given that the man invests equally in both the companies, Let us assume that the investment made by the man in each company be $₹ z$ .
As $N u m b e r o f s h a r e s = \frac{I n v e s t m e n t}{M a r k e t v a l u e}$ ,
∴ $A n n u a l i n c o m e, A_{x} = N u m b e r o f s h a r e s \times F a c e v a l u e \times \frac{D i v i d e n d}{100} = \frac{z}{M_{x}} \times F_{x} \times \frac{D_{x}}{100}$
$A_{x} = \frac{z}{120} \times 100 \times \frac{5}{100} = ₹ \frac{z}{24}$
Step 3: Calculate the annual income of Company Y
As shares of Company Y are at a discount of $10 %$
∴ $M a r k e t v a l u e, M_{y} = F a c e v a l u e + P r e m i u m % o f F a c e v a l u e = F_{y} - d_{y} % o f F_{y}$
$M_{y} = 100 - \frac{10}{100} \times 100 = 100 - 10 = ₹ 90$
As $N u m b e r o f s h a r e s = \frac{I n v e s t m e n t}{M a r k e t v a l u e}$ ,
∴ $A n n u a l i n c o m e, A_{y} = N u m b e r o f s h a r e s \times F a c e v a l u e \times \frac{D i v i d e n d}{100} = \frac{z}{M_{y}} \times F_{y} \times \frac{D_{y}}{100}$
$A_{y} = \frac{z}{90} \times 100 \times \frac{7}{100} = ₹ \frac{7 z}{90}$
Step 4: Calculate the sum of the annual incomes of Company X and Y
It is given that the sum of annual incomes of Company X and Company Y is $₹ 1290$
∴ $S u m o f a n n u a l i n c o m e s = A_{x} + A_{y}$
$1290 = \frac{z}{24} + \frac{7 z}{90} 1290 = \frac{z}{24} + \frac{7 z}{90} 1290 = \frac{1}{6} (\frac{z}{4} + \frac{7 z}{15}) 1290 = \frac{1}{6} (\frac{15 z + 7 z \times 4}{60}) 1290 = \frac{1}{6} (\frac{15 z + 28 z}{60}) 1290 = \frac{1}{6} \times \frac{43 z}{60} z = \frac{1290 \times 60 \times 6}{43} z = ₹ 10800$
Step 5: Calculate the total investment done by the man
As it is given that the man invests equally in both the companies
∴ $T o t a l i n v e s t m e n t = 2 \times z$
$= 2 \times 10800 = ₹ 21600$
∴ Total investment done by man in Company X and Company Y is $₹ 21600$ . Hence, Option D is correct.

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