if 5(3^a-1 + 1),(6^2a-3 + 2),7(5^a-1 + 5) are in AP then what is the value of a
Answers
Step-by-step explanation:
Example 2: A man invests in shares for which we have the condition “7% Rs 100 shares at Rs 120”. What is the annual income of a person holding 150 such shares? Also, find his annual profit percentage.
Solution: Given,
Rate of dividend=7%
Nominal value (NV) = Rs 100
Market value (MV) = Rs 120
No. of shares= 150
Therefore, Income =No. of shares
\times rate of dividend
\times NV=
Rs \: (150 \times \dfrac{7}{100} \times 100)=Rs \: 1050
First we need to find the sum invested to find the profit percentage.
Investment=No. of shares
\times MV=
Rs \: (150 \times 120)=Rs \: 18000
Therefore, Required profit percentage
=\dfrac{Income}{Investment} \times 100 \% =\dfrac{Rs \: 1050}{Rs \: 18000} \times 100=5\dfrac{5}{6} \%
Example 3: Which is a better investment: 16% at 80 or 20% at 120?
Solution: 16% at 80 means MV of 1 share is Rs 80, NV of 1 share is Rs100 and dividend paid is 16%.
Similarly, 20% at 120 means MV of 1 share is Rs 120, NV of 1 share is Rs 100 and dividend paid is 20%.
Case 1:
Income on Rs 80=16% of Rs 100=Rs 16
Therefore, income on
Re \: 1=Rs \: \dfrac{16}{80}= Rs \: 0.20
Case 2:
Income on Rs 120=20% of Rs 100= Rs 20
Therefore, income on
Re \: 1=Rs \: \dfrac{20}{120}= Rs \: 0.16
Therefore, the first investment is better.
Example 4: A company declares semiannual dividend of 6%. A man has 500 shares of NV Rs 25 each. Find his annual income.
Solution: Total NV of shares= Rs(25
\times 500)= Rs 12500
Semiannual dividend = 6% of Rs 12500=
\dfrac{6}{100} \times 12500=Rs \: 750
Therefore, his annual income= Rs (750
\times 2)=Rs 1500
Example 5: Divide Rs 29184 into two parts such that if one part is invested in 12%, Rs 100 shares at 4% discount and the other in 15%, Rs 100 shares at 8% premium, the annual incomes are equal.
Solution: Let the investment in 12%, Rs 100 shares at 4% discount be
Rs \: x .