Question

Raghav invests Rs. 12,000 partly in 10% (Rs. 80) shares at Rs. 120 and partly in 5% (Rs. 100) shares at Rs. 150. If his total income is Rs. 500, then how much he invested in each?


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Answer 1

Answer:

mark a Brinlet please ❣️

Answer 2

$\large\underline{\sf{Solution-}}$

Let assume that Raghav invested in 10% (Rs. 80) shares at Rs. 120 be Rs x .

So, his investment in 5% (Rs. 100) shares at Rs. 150 be Rs 12000 - x.

Now,

Case :- 1

Face value of share = Rs 80

Dividend % = 10 %

So, Income on 1 share = 10 % of 80 = Rs 8.

Market value of 1 share = Rs 120

Investment = Rs x

So,

$\rm :\longmapsto\:Income \: on \: 1 \: share \: of \: Rs \: 120 = Rs \: 8$

Thus,

$\rm :\longmapsto\:Income \: on \: Rs \: x = \dfrac{8}{120} \times x = Rs \: \dfrac{x}{15}$

Case :- 2

Face value of share = Rs 100

Dividend % = 5 %

So, Income on 1 share = 5 % of 100 = Rs 5.

Market value of 1 share = Rs 150

Investment = Rs 12000 - x

So,

$\rm :\longmapsto\:Income \: on \: 1 \: share \: of \: Rs \: 150 = Rs \: 5$

Thus,

$\rm :\longmapsto\:Income \: on \: Rs \: 12000 - x = \dfrac{5}{150} \times (12000 - x) = Rs \: \dfrac{(12000 - x)}{30}$

Now,

According to statement,

Total annual Income = Rs 500

Thus,

$\rm :\implies\:\dfrac{x}{15} + \dfrac{12000 - x}{30} = 500$

$\rm :\longmapsto\:\dfrac{2x + 12000 - x}{30} = 500$

$\rm :\longmapsto\:\dfrac{x + 12000}{30} = 500$

$\rm :\longmapsto\:x + 12000 = 15000$

$\rm :\longmapsto\:x = 15000 - 12000$

$\bf\implies \:x = 3000$

So,

The Investment in 10% (Rs. 80) shares at Rs. 120 = Rs 3000

and

The investment in 5% (Rs. 100) shares at Rs. 150 be Rs 12000 - 3000 = Rs 9000.