Pramod wants to invest $₹ 35000$ in shares, such that the percentage return on his investment is $8 \frac{1}{7} %$ . He invested $₹ 6000$ in $6 %$ , $₹ 50$ shares of 'Lakme' at $₹ 40$ , $₹ 15000$ in $8 %$ , $₹ 100$ shares of 'Volta' at $₹ 125$ and the remaining in $12 %$ , $₹ 150$ shares of 'BPL'. At what rate did he buy the 'BPL' shares?

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Solution

Step 1: Given data:
Total investment, $I = ₹ 35000$
Return%, $r % = 8 \frac{1}{7} %$
Type of data Lakme Volta BPL
Investment $I_{1}$ is $₹ 6000$ $I_{2}$ is $₹ 15000$ $I_{3}$ is $(I - I_{1} - I_{2}) = (35000 - 6000 - 15000) = ₹ 14000$
Nominal value $F_{1}$ is $₹ 50$ $F_{2}$ is $₹ 100$ $F_{3}$ is $₹ 150$
Market value $M_{1}$ is $₹ 40$ $M_{2}$ is $₹ 125$ Not given
Rate of dividend $D_{1}$ is $6 %$ $D_{2}$ is $8 %$ $D_{3}$ is $12 %$
Step 2: Find the annual income from Lakme shares:
Pramod invested $₹ 6000$ in $6 %$ , $₹ 50$ shares of 'Lakme' at $₹ 40$ . To calculate annual income, the number of shares is required.
∴ $N u m b e r o f s h a r e s = \frac{I n v e s t m e n t}{M a r k e t v a l u e}$
$N_{1} = \frac{I_{1}}{M_{1}} = \frac{6000}{40} = 150 shares$
Now,
$A n n u a l i n c o m e = N u m b e r o f s h a r e s \times N o m i n a l v a l u e \times \frac{R a t e o f d i v i d e n d}{100}$
$A_{1} = N_{1} \times F_{1} \times \frac{D_{1}}{100} = 150 \times 50 \times \frac{6}{100} = ₹ 450$
Step 3: Find the annual income from Volta shares:
Pramod invested $₹ 15000$ in $8 %$ , $₹ 100$ shares of 'Volta' at $₹ 125$ . To calculate annual income, the number of shares is required.
∴ $N u m b e r o f s h a r e s = \frac{I n v e s t m e n t}{M a r k e t v a l u e}$
$N_{2} = \frac{I_{2}}{M_{2}} = \frac{15000}{125} = 120 shares$
Now,
$A n n u a l i n c o m e = N u m b e r o f s h a r e s \times N o m i n a l v a l u e \times \frac{R a t e o f d i v i d e n d}{100}$
$A_{2} = N_{2} \times F_{2} \times \frac{D_{2}}{100} = 120 \times 100 \times \frac{8}{100} = ₹ 960$
Step 4: Find the annual income from BPL shares:
As for BPL shares, Pramod invested $₹ 14000$ in $₹ 150$ shares of $12 %$ .
Also, Pramod's total return percent is $8 \frac{1}{7} %$ of his investment.
∴ $R e t u r n % = \frac{T o t a l A n n u a l I n c o m e}{T o t a l I n v e s t m e n t} \times 100$
$r % = \frac{T o t a l A n n u a l I n c o m e}{I} \times 100 8 \frac{1}{7} = \frac{T o t a l A n n u a l I n c o m e}{35000} \times 100 \frac{57}{7} = \frac{T o t a l A n n u a l I n c o m e}{350} T o t a l A n n u a l I n c o m e = \frac{57 \times 350}{7} T o t a l A n n u a l I n c o m e = ₹ 2850$
Let us assume that the annual income from BPL shares be $A_{3}$ .
∴ $T o t a l A n n u a l i n c o m e = A_{1} + A_{2} + A_{3}$
$2850 = 450 + 960 + A_{3} 2850 = 1410 + A_{3} A_{3} = 2850 - 1410 A_{3} = ₹ 1440$
Step 5: Find the number of shares in BPL shares:
Let us assume that the number of shares in BPL shares be $N_{3}$ .
∴ $A n n u a l i n c o m e = N u m b e r o f s h a r e s \times N o m i n a l v a l u e \times \frac{R a t e o f d i v i d e n d}{100}$
$A_{3} = N_{3} \times F_{3} \times \frac{D_{3}}{100} 1440 = N_{3} \times 100 \times \frac{12}{100} N_{3} = \frac{1440}{12} N_{3} = 120 shares$
Step 6: Find the market value of the shares of BPL:
$M a r k e t v a l u e = \frac{I n v e s t m e n t}{N u m b e r o f s h a r e s}$
$M_{3} = \frac{I_{3}}{N_{3}} = \frac{14000}{120} = ₹ 116 \frac{2}{3}$
Final Answer: Hence, Pramod bought the shares of $12 %$ at $₹ 116.67$ or $₹ 116 \frac{2}{3}$ .

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Type of data	Lakme	Volta	BPL
Investment	$I_{1}$ is $₹ 6000$	$I_{2}$ is $₹ 15000$	$I_{3}$ is $(I - I_{1} - I_{2}) = (35000 - 6000 - 15000) = ₹ 14000$
Nominal value	$F_{1}$ is $₹ 50$	$F_{2}$ is $₹ 100$	$F_{3}$ is $₹ 150$
Market value	$M_{1}$ is $₹ 40$	$M_{2}$ is $₹ 125$	Not given
Rate of dividend	$D_{1}$ is $6 %$	$D_{2}$ is $8 %$	$D_{3}$ is $12 %$