## What are some CAT Stocks & Shares Practice Questions?

**Q1.** Find the annual income derived from â‚¹ 2500, 8% stock at 106.

**Answer:** â‚¹ 200

**Solution:** Annual income = (Rate of interest / 100) × Face value of the stock

Annual income = (8 / 100) × â‚¹ 2500 = â‚¹ 200

**Q2.** Find the annual income derived by investing â‚¹ 6800 in 10% stock at 136.

**Answer:** â‚¹ 500

**Solution: **Annual income = (Rate of interest / 100) × (Amount invested / Market price) × Face value

Annual income = (10 / 100) × (â‚¹ 6800 / 136) × â‚¹ 100 = â‚¹ 500

**Q3.** Find the cost of 96 shares of â‚¹ 10 each at 3/4 discount, brokerage being 1/4 per share.

**Answer**: â‚¹ 264

**Solution**: Total cost = [Number of shares × (Face value - Face value × Discount)] + (Number of shares × Brokerage per share)

Total cost = [96 × (â‚¹ 10 - â‚¹ 10 × 3/4)] + (96 × â‚¹ 0.25)

Total cost = (96 × â‚¹ 2.50) + (96 × â‚¹ 0.25) = â‚¹ 240 + â‚¹ 24 = â‚¹ 264

**Q4.** Ravi invested â‚¹ 913 partly in 4% stock at â‚¹ 97 and partly in 5% stock at â‚¹ 107. If his income form both is equal, find the amount invested in each stock.

**Answer:** â‚¹ 74.42

**Solution:** Let the amount invested in 4% stock be x.

(4/100) × (x/97) × 100 = (5/100) × ((â‚¹ 913 - x)/107) × 100

x ≈ â‚¹ 838.58

Amount invested in 5% stock ≈ â‚¹ 913 - â‚¹ 838.58 ≈ â‚¹ 74.42

## What are the must-do Stocks & Shares questions for the CAT exam?

**Q5**. A man buys â‚¹ 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:** â‚¹ 22.50

**Solution**: (Dividend rate / 100) × Face value of each share = (Return on investment / 100) × Price of each share

(9 / 100) × â‚¹ 25 = (10 / 100) × x

x = (â‚¹ 2.25 / 0.1) = â‚¹ 22.50

**Q6**. A man sells â‚¹ 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 â‚¹ 70. How much of the proceeds were invested in each stock?

**Answer**: â‚¹ 4200

**Solution:** Let the amount invested in 8% stock be x.

(8/100) × (x/90) × 100 + (9/100) × ((â‚¹ 7800 - x)/108) × 100 - (12/100) × â‚¹ 5000 = â‚¹ 70

x = â‚¹ 3600

Amount invested in 9% stock = â‚¹ 7800 - â‚¹ 3600 = â‚¹ 4200

**Q7.** The cost price of a â‚¹ 100 stock at 4 discount, when brokerage is 1/4 % is.

**Answer:** â‚¹ 96.25

**Solution**: Cost price = Face value - (Face value × Discount) + (Face value × Brokerage)

Cost price = â‚¹ 100 - (â‚¹ 100 × 4/100) + (â‚¹ 100 × (1/4)/100)

Cost price = â‚¹ 100 - â‚¹ 4 + â‚¹ 0.25 = â‚¹ 96.25

**Q8.** How many shares of market value â‚¹ 25 each can be purchased for â‚¹ 12750, brokerage being 2%?

**Answer:** 499

**Solution**: Number of shares = (Total amount - (Total amount × Brokerage)) ÷ Market value of each share

Number of shares = (â‚¹ 12750 - (â‚¹ 12750 × 2/100)) ÷ â‚¹ 25

Number of shares = â‚¹ 12495 ÷ â‚¹ 25 = 499.8, rounded down to 499

## What were the previous year's CAT Stocks & Shares questions?

**Q9**. A man invests in a 16% stock at 128. The interest obtained by him is

**Answer:** â‚¹ 20.48

**Solution**: Interest on actual investment = (Rate of interest × Market price) ÷ 100

Interest on actual investment = (16 × â‚¹ 128) ÷ 100 = â‚¹ 20.48

**Q10.** The income derived from a â‚¹ 100, 13% stock at â‚¹ 105, is

**Answer: **12.38%

**Solution:** Income = (Rate of interest ÷ (Market price ÷ Face value)) × 100

Income = (13 ÷ (â‚¹ 105 ÷ â‚¹ 100)) × 100

Income = (13 ÷ 1.05) × 100 ≈ 12.38%

**Q11.** A person has deposited â‚¹ 13200 in a bank which pays 14% interest. He withdraws the money and invests in â‚¹ 100 stock at â‚¹ 110 which pays a dividend of 15%. How much does he gain or lose?

**Answer:** -â‚¹ 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 = ((â‚¹ 13200 ÷ â‚¹ 110) × â‚¹ 100 × 15 ÷ 100) - ((â‚¹ 13200 × 14) ÷ 100)

Gain or loss = â‚¹ 1800 - â‚¹ 1848 = -â‚¹ 48 (loss)

**Q12**. A 6% stock yields 8%. The market value of the stock is

**Answer: **â‚¹ 75

**Solution: **Market value = (Nominal rate of interest ÷ Actual rate of interest) × Face value

Market value = (6 ÷ 8) × â‚¹ 100 = 0.75 × â‚¹ 100 = â‚¹ 75

## What were the Stocks & Shares questions on the CAT 2022 exam?

**Q13.** â‚¹ 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 ≈ â‚¹ 8941.61

**Solution:** Let the investment in 9% stock be x.

(9/100) × (x/75) × 100 = (10/100) × ((â‚¹ 9800 - x)/80) × 100

x ≈ â‚¹ 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 â‚¹ 100, paying a dividend of 8% so that my yield is 11%?

**Answer:** â‚¹ 72.73

**Solution:** Price = (Dividend ÷ Yield) × Face value

Price = (8 ÷ 11) × â‚¹ 100 ≈ 0.7273 × â‚¹ 100 ≈ â‚¹ 72.73

**Q16.** A man buys â‚¹ 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:** â‚¹ 40

**Solution:** (Dividend rate × Face value of each share) ÷ Price of each share = Return on investment

(10/100) × â‚¹ 50 ÷ x = 12.5/100

x = (10/100) × â‚¹ 50 ÷ (12.5/100) = â‚¹ 5 ÷ 0.125 = â‚¹ 40

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