Mamta and Sonia invested equal amounts in buying shares of two different companies. Mamta bought shares of Hindalco paying a dividend of $14 %$ on its $₹ 125$ share available in the market for $₹ 140$ , while Sonia bought shares of HLL paying a dividend of $13 %$ on its $₹ 300$ share available in the market for $₹ 260$ . If Sonia's annual income is $₹ 1820$ more than that of Mamta, then find the amount invested by each of them.

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Solution

Step 1: Given Data:
Face value of Hindalco, $F_{1} = ₹ 125$
Market value of Hindalco, $M_{1} = ₹ 140$
Rate of dividend of Hindalco, $D_{1} = 14 %$
Face value of HLL, $F_{2} = ₹ 300$
Market value of HLL, $M_{2} = ₹ 260$
Rate of dividend of HLL, $D_{2} = 13 %$
Sonia's annual income - Mamta's annual income $= ₹ 1820$
Step 2: Calculate the income for one share of Hindalco
$I n c o m e = \frac{R a t e o f d i v i d e n d}{100} \times F a c e v a l u e$
$I_{1} = \frac{D_{1}}{100} \times F_{1} = \frac{14}{100} \times 125 = ₹ 17.5$
Step 3: Calculate the income for one share of HLL
$I n c o m e = \frac{R a t e o f d i v i d e n d}{100} \times F a c e v a l u e$
$I_{2} = \frac{D_{2}}{100} \times F_{2} = \frac{13}{100} \times 300 = ₹ 39$
Step 4: Calculate the annual income from Hindalco
As Mamta and Sonia invested equally in both the companies, let money invested in each company $₹ y$
$N o o f s h a r e s = \frac{I n v e s t m e n t}{M a r k e t v a l u e} = \frac{y}{M_{1}} = \frac{y}{140} shares$
∴ $T o t a l a n n u a l i n c o m e = N u m b e r o f s h a r e s \times I n c o m e f r o m o n e s h a r e$
$A_{1} = \frac{y}{140} \times 17.5 [∵ i n c o m e c a l c u l a t e d i n s t e p 2] A_{1} = ₹ \frac{y}{8}$
Step 5: Calculate the annual income from HLL
$N o o f s h a r e s = \frac{I n v e s t m e n t}{M a r k e t v a l u e} = \frac{y}{M_{2}} = \frac{y}{260} shares$
∴ $T o t a l a n n u a l i n c o m e = N u m b e r o f s h a r e s \times I n c o m e f r o m o n e s h a r e$
$A_{2} = \frac{y}{260} \times 39 [∵ i n c o m e c a l c u l a t e d i n s t e p 3] A_{2} = ₹ \frac{3 y}{20}$
Step 6: Calculate the investment done by Mamta and Sonia
(ii) It is given that the difference between the returns from both the companies is $₹ 1820$
∴ $D i f f e r e n c e i n a n n u a l i n c o m e = S o n i a' s a n n u a l i n c o m e - M a m t a' s a n n u a l i n c o m e$
$1820 = A_{2} - A_{1} 1820 = \frac{3 y}{20} - \frac{y}{8} 1820 = \frac{3 y \times 8 - y \times 20}{160} 1820 = \frac{24 y - 20 y}{160} 1820 = \frac{4 y}{160} 1820 = \frac{y}{40} y = 1820 \times 40 y = ₹ 72800$
Final Answer: Hence, the amount invested by each of them is $₹ 72800$ .

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