Mathematics
Mr. Gautam sold a certain number of ₹ 20 shares paying 8% dividend at ₹ 18 and invested the proceed in ₹ 10 shares paying 12% dividend at 50% premium. If the change in his annual income is ₹ 120, find the number of shares sold by Mr. Gautam.
Shares & Dividends
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Answer
Let the number of shares Mr. Gautam sold be x.
For initial shares,
N.V. = ₹ 20
Rate of dividend = 8%
By formula,
Annual income (from first investment) = No. of shares × Rate of div. × N.V. of 1 share
= x × × 20
=
S.P. of each share = ₹ 18.
Amount obtained on selling shares = S.P × No. of shares = ₹ 18x.
The proceeds he invested in ₹ 10 shares at ₹ 15, paying 12% dividend.
N.V. = ₹ 10
Premium = 50% of ₹ 10 = = 5
M.V. = N.V. + Premium = ₹ 10 + 5 = ₹ 15
Number of shares =
The change in Mr. Gautam's annual income = ₹ 120
By formula,
Annual income (from second investment) = No. of shares × Rate of div. × N.V. of 1 share
=
=
Given, change in income = ₹ 120
Hence, Mr. Gautam sold 750 shares.
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Related Questions
Anaya invests a sum of money in ₹ 50 shares, paying 15% dividend quoted at 20% premium. If her annual dividend is ₹ 600, calculate :
(i) the number of shares she bought.
(ii) her total investment.
(iii) the rate of return on her investment.
₹100 shares of a company giving 10% dividend are selling at ₹150. Mr. Saha invests ₹ 18,000 to buy these shares. He sells 80% of his shares after one year. Find :
(a) the number of shares he purchased.
(b) the number of shares he sold.
(c) his annual income from the remaining 20% shares he still holds.
A man invests ₹ 50,000 of his savings in 12%, ₹ 100 shares at ₹ 125 another ₹ 60,000 in 15%, ₹ 100 shares at ₹ 120 and remainder 18% ₹ 100 shares at ₹ 140. If his annual income is ₹ 21,300 find :
(i) the rate of return on the whole.
(ii) the investment in third company.
Case study:
Share market is a place where investors trade different instruments like stocks, mutual funds, etc.It is a place where companies sell parts (called shares) of their companies and investors buy them in expectation of greater returns.
Mr. Reddy wants to invest his money in company which gives a better return. He has following options:
Company X : ₹ 100 shares are available at ₹ 120 with a dividend of 8% p.a.
Company Y : ₹ 10 shares are available at ₹ 8 with a dividend of 6% p.a.
Based on the above information, answer the following questions :
(i) If Mr. Reddy wants to invest ₹ 15,000 in company X, then what will be his Annual Income ?
(ii) If Mr. Reddy wants to invest ₹ 15,000 in company Y, then what will be his Annual Income ?
(iii) Which company is a better option for Mr. Reddy to invest in ?