What are some CAT Stocks & Shares Practice Questions?
Q1. Find the annual income derived from ₹ 2500, 8% stock at 106.
Answer: ₹ 200
Solution: Annual income = (Rate of interest / 100) × Face value of the stock
Annual income = (8 / 100) × ₹ 2500 = ₹ 200
Q2. Find the annual income derived by investing ₹ 6800 in 10% stock at 136.
Answer: ₹ 500
Solution: Annual income = (Rate of interest / 100) × (Amount invested / Market price) × Face value
Annual income = (10 / 100) × (₹ 6800 / 136) × ₹ 100 = ₹ 500
Q3. Find the cost of 96 shares of ₹ 10 each at 3/4 discount, brokerage being 1/4 per share.
Answer: ₹ 264
Solution: Total cost = [Number of shares × (Face value - Face value × Discount)] + (Number of shares × Brokerage per share)
Total cost = [96 × (₹ 10 - ₹ 10 × 3/4)] + (96 × ₹ 0.25)
Total cost = (96 × ₹ 2.50) + (96 × ₹ 0.25) = ₹ 240 + ₹ 24 = ₹ 264
Q4. Ravi invested ₹ 913 partly in 4% stock at ₹ 97 and partly in 5% stock at ₹ 107. If his income form both is equal, find the amount invested in each stock.
Answer: ₹ 74.42
Solution: Let the amount invested in 4% stock be x.
(4/100) × (x/97) × 100 = (5/100) × ((₹ 913 - x)/107) × 100
x ≈ ₹ 838.58
Amount invested in 5% stock ≈ ₹ 913 - ₹ 838.58 ≈ ₹ 74.42
What are the must-do Stocks & Shares questions for the CAT exam?
Q5. A man buys ₹ 25 shares in a company which pays 9% dividend. The money invested is such that it gives 10% on investment. At what price did he buy the shares?
Answer: ₹ 22.50
Solution: (Dividend rate / 100) × Face value of each share = (Return on investment / 100) × Price of each share
(9 / 100) × ₹ 25 = (10 / 100) × x
x = (₹ 2.25 / 0.1) = ₹ 22.50
Q6. A man sells ₹ 5000, 12% stock at 156 and invests the proceeds partly in 8% stock at 90 and 9% stock at 108. He thereby increases his income by ₹ 70. How much of the proceeds were invested in each stock?
Answer: ₹ 4200
Solution: Let the amount invested in 8% stock be x.
(8/100) × (x/90) × 100 + (9/100) × ((₹ 7800 - x)/108) × 100 - (12/100) × ₹ 5000 = ₹ 70
x = ₹ 3600
Amount invested in 9% stock = ₹ 7800 - ₹ 3600 = ₹ 4200
Q7. The cost price of a ₹ 100 stock at 4 discount, when brokerage is 1/4 % is.
Answer: ₹ 96.25
Solution: Cost price = Face value - (Face value × Discount) + (Face value × Brokerage)
Cost price = ₹ 100 - (₹ 100 × 4/100) + (₹ 100 × (1/4)/100)
Cost price = ₹ 100 - ₹ 4 + ₹ 0.25 = ₹ 96.25
Q8. How many shares of market value ₹ 25 each can be purchased for ₹ 12750, brokerage being 2%?
Answer: 499
Solution: Number of shares = (Total amount - (Total amount × Brokerage)) ÷ Market value of each share
Number of shares = (₹ 12750 - (₹ 12750 × 2/100)) ÷ ₹ 25
Number of shares = ₹ 12495 ÷ ₹ 25 = 499.8, rounded down to 499
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Q9. A man invests in a 16% stock at 128. The interest obtained by him is
Answer: ₹ 20.48
Solution: Interest on actual investment = (Rate of interest × Market price) ÷ 100
Interest on actual investment = (16 × ₹ 128) ÷ 100 = ₹ 20.48
Q10. The income derived from a ₹ 100, 13% stock at ₹ 105, is
Answer: 12.38%
Solution: Income = (Rate of interest ÷ (Market price ÷ Face value)) × 100
Income = (13 ÷ (₹ 105 ÷ ₹ 100)) × 100
Income = (13 ÷ 1.05) × 100 ≈ 12.38%
Q11. A person has deposited ₹ 13200 in a bank which pays 14% interest. He withdraws the money and invests in ₹ 100 stock at ₹ 110 which pays a dividend of 15%. How much does he gain or lose?
Answer: -₹ 48 (loss)
Solution: Gain or loss = ((Amount deposited ÷ Market price of the stock) × Face value × Dividend ÷ 100) - ((Amount deposited × Bank interest rate) ÷ 100)
Gain or loss = ((₹ 13200 ÷ ₹ 110) × ₹ 100 × 15 ÷ 100) - ((₹ 13200 × 14) ÷ 100)
Gain or loss = ₹ 1800 - ₹ 1848 = -₹ 48 (loss)
Q12. A 6% stock yields 8%. The market value of the stock is
Answer: ₹ 75
Solution: Market value = (Nominal rate of interest ÷ Actual rate of interest) × Face value
Market value = (6 ÷ 8) × ₹ 100 = 0.75 × ₹ 100 = ₹ 75
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Q13. ₹ 9800 are invested partly in 9% stock at 75 and 10% stock at 80 to have equal amount of incomes. The investment in 9% stock is
Answer: x ≈ ₹ 8941.61
Solution: Let the investment in 9% stock be x.
(9/100) × (x/75) × 100 = (10/100) × ((₹ 9800 - x)/80) × 100
x ≈ ₹ 8941.61
Q14. A man invests some money partly in 9% stock at 96 and partly in 12% stock at 120. To obtain equal dividends from both, he must invest the money in the ratio
Answer: 15x : 16y
Solution: Let the ratio of investment in 9% stock to 12% stock be x:y.
(9/100) × (x/96) × 100 = (12/100) × (y/120) × 100
1080x = 1152y
Simplifying the ratio by dividing both sides by 72, we get:
15x : 16y
Q15. At what price should I buy a share the value of which is ₹ 100, paying a dividend of 8% so that my yield is 11%?
Answer: ₹ 72.73
Solution: Price = (Dividend ÷ Yield) × Face value
Price = (8 ÷ 11) × ₹ 100 ≈ 0.7273 × ₹ 100 ≈ ₹ 72.73
Q16. A man buys ₹ 50 shares in a company which pays 10% dividend. If the man gets 12.5% on his investment, at what price did he buy the shares?
Answer: ₹ 40
Solution: (Dividend rate × Face value of each share) ÷ Price of each share = Return on investment
(10/100) × ₹ 50 ÷ x = 12.5/100
x = (10/100) × ₹ 50 ÷ (12.5/100) = ₹ 5 ÷ 0.125 = ₹ 40
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