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 follow these steps:

Step 1: Calculate the dividend received from ABC Ltd shares.
Atul invested Rs 75,000 in buying Rs 200 shares of ABC Ltd. The dividend paid by ABC Ltd is 20%.
So, the dividend received from ABC Ltd shares is (75,000 * 20%) = Rs 15,000.

Step 2: Calculate the yield on investment for ABC Ltd shares.
The yield on investment is given as 16%.
So, the yield amount is (75,000 * 16%) = Rs 12,000.

Step 3: Calculate the selling price of ABC Ltd shares after one year.
Atul sold the ABC Ltd shares at Rs 350 per share, and he had a total of Rs 200 shares.
So, the selling price of ABC Ltd shares is (350 * 200) = Rs 70,000.

Step 4: Calculate the total amount invested in XYZ Ltd shares.
The total amount invested in XYZ Ltd shares is the sum of the selling price of ABC Ltd shares after one year and the dividend received from ABC Ltd shares.
So, total amount invested in XYZ Ltd shares = Rs (70,000 + 15,000) = Rs 85,000.

Step 5: Calculate the dividend received from XYZ Ltd shares.
The dividend paid by XYZ Ltd is 16%.
So, the dividend received from XYZ Ltd shares is (85,000 * 16%) = Rs 13,600.

Step 6: Calculate the increased annual income.
Atul increased his annual income by Rs 2400.
So, increased annual income = Rs 2400.

Step 7: Calculate the rate at which Atul bought XYZ Ltd shares.
The rate at which Atul bought XYZ Ltd shares can be found by dividing the increased annual income by the dividend paid by XYZ Ltd.
So, the rate at which Atul bought XYZ Ltd shares = (2400 / 13,600) ≈ 0.1765 or 17.65%.

Therefore, Atul bought the XYZ Ltd shares at a rate of 17.65%.