Atul invested Rs 75000 in buying Rs 200 shares of ABC Ltd paying a dividend of 20%. He bought them at a rate which gave him a yield of 16%. After a year he sold them at Rs 350 and invested the proceeds along with the dividend obtained in buying Rs 175 shares of XYZ ltd paying a dividend of 16%. He thereby increased his annual income by Rs 2400. Find the rate at which he bought XYZ ltd shares
To find the rate at which Atul bought XYZ Ltd shares, we need to break down the given information and solve for the unknown.
Let's start solving this step by step:
1. Find the dividend received from ABC Ltd:
Atul invested Rs 75,000 in buying Rs 200 shares of ABC Ltd, which paid a dividend of 20%. The dividend received can be calculated as:
Dividend received = Total Investment * Dividend Rate
= Rs 75,000 * 0.20
= Rs 15,000
2. Calculate Atul's yield from ABC Ltd:
The yield is the income generated from an investment, expressed as a percentage of the investment amount. Here, Atul's yield from ABC Ltd is given as 16%. We can calculate the income he earned from the investment as:
Income from ABC Ltd = Total Investment * Yield Rate
= Rs 75,000 * 0.16
= Rs 12,000
3. Calculate the selling price of ABC Ltd shares after a year:
Atul sold the ABC Ltd shares at Rs 350 each. Since he bought Rs 200 shares, the total selling price can be calculated as:
Total Selling Price = Selling Price * Number of Shares
= Rs 350 * 200
= Rs 70,000
4. Calculate the amount invested in XYZ Ltd shares:
Atul invested the proceeds (Rs 70,000) from selling ABC Ltd shares along with the dividend received (Rs 15,000) in buying shares of XYZ Ltd. Therefore, the total investment in XYZ Ltd can be calculated as:
Total Investment in XYZ Ltd = Proceeds from Selling ABC Ltd + Dividend from ABC Ltd
= Rs 70,000 + Rs 15,000
= Rs 85,000
5. Calculate the increased annual income from XYZ Ltd:
Atul increased his annual income by Rs 2400 by investing in XYZ Ltd. Therefore, the income from XYZ Ltd can be calculated as:
Income from XYZ Ltd = Total Investment in XYZ Ltd * Dividend Rate
= Rs 85,000 * 0.16
= Rs 13,600
Now, we can determine the rate at which he bought XYZ Ltd shares by dividing the income by the total investment:
Rate = Income from XYZ Ltd / Total Investment in XYZ Ltd
= Rs 13,600 / Rs 85,000
≈ 0.16 (approximately)
Therefore, the rate at which he bought XYZ Ltd shares is approximately 0.16 or 16%.