IBPS PO Quantitative Aptitude: Simple and Compound Interest questions with solutions

Q1. A man invested Rs. X in simple interest at a rate of 15% for 5 years. Then he invested X + 300 at compound interest at 10% per annum for 2 years. If the total interest obtained is Rs. 4383, find the total amount invested by the man.

1. 9000
2. 8700
3. 8500
4. 9300

Answer: 9300

The simple interest on X for 5 years at 15% is \(\frac{X\cdot15\cdot5}{100} = 0.75X\). The compound interest on \(X+300\) for 2 years at 10% is \((X+300)(1.21-1)=0.21(X+300)\). Solving \(0.75X + 0.21(X+300)=4383\) gives \(X=4500\), so the total amount invested is \(X+(X+300)=9300\).

Q2. Veer invested Rs. 10,000 at simple interest for 2 years at the rate of R% and got an interest of Rs. 1,400. He invested the total amount (principal + interest) in a scheme that offered compound interest at the rate of (R% + x%) for 2 years. What are the possible integral values of x% so that the compound interest is less than Rs. 2,400? (i) 1% (ii) 2% (iii) 3% (iv) 4% (v) 5%

1. Only (i)
2. Only (i), (ii)
3. Only (i), (ii) and (iii)
4. Only (i), (ii), (iii) and (iv)

Answer: Only (i), (ii) and (iii)

From simple interest, 1400 = 10000 × R × 2 / 100, so R = 7%. The new principal is 11,400 and the compound rate is (7 + x)%. Checking x = 1, 2, 3, 4, 5 shows that CI remains below Rs. 2,400 only for x = 1, 2, 3.

Q3. Q80. A man invested Rs. 7500 for two years at a rate of $X\%$ p.a. on compound interest and received total interest of Rs. 3300. He invested Rs. 4800 in scheme A, which offers simple interest for two years at the rate of ____% p.a., and he also invested Rs. ____ in scheme B, which offers simple interest for two years at the rate of 12% p.a. The total interest received from scheme A is Rs. ____ more than that from scheme B. Which of the following option(s) is/are correct in the blank spaces? (i) $(X-5), 200X, 480$ (ii) $X, 4800, 360$ (iii) $1.5X, 4000, 500$ A) None of these B) Only (i) C) Only (iii) D) Only (i) & (ii) E) Only (i) & (iii)

1. None of these
2. Only (i)
3. Only (iii)
4. Only (i) & (ii)
5. Only (i) & (iii)

Answer: Only (i)

From the compound interest on Rs. 7500 for 2 years, the rate $X$ can be determined. Then each proposed set of blanks is checked using simple interest formulas for schemes A and B. Only option (i) satisfies all conditions.

Q4. A man purchased a cow for Rs. 3000 and sold it the same day for Rs. 3600, allowing the buyer a credit of 2 years. If the rate of interest is 10% per annum, then the man has a gain of:

1. 0%
2. 5%
3. 7.5%
4. 10%

Answer: 0%

The selling price of Rs. 3600 payable after 2 years has a present value of Rs. 3000 at 10% simple interest. Since the present value equals the purchase price, there is no gain or loss.

Q5. The true discount on Rs. 2562 due 4 months hence is Rs. 122. The rate percent is:

1. 12%
2. 13 1/3%
3. 15%
4. 14%

Answer: 15%

If the true discount is Rs. 122 on Rs. 2562, then the present worth is Rs. 2440. Using simple interest for 4 months, the rate comes out to 15% per annum.

Q6. A trader owes a merchant Rs. 10,028 due 1 year hence. The trader wants to settle the account after 3 months. If the rate of interest is 12% per annum, how much cash should he pay?

1. Rs. 9025.20
2. Rs. 9200
3. Rs. 9600
4. Rs. 9560

Answer: Rs. 9200

The debt of Rs. 10,028 is due after 1 year, but payment is made after 3 months, so the remaining time is 9 months. Discounting the amount for 9 months at 12% per annum gives Rs. 9200.

Q7. A man wants to sell his scooter. There are two offers: one at Rs. 12,000 cash and the other a credit of Rs. 12,880 to be paid after 8 months, money being at 18% per annum. Which is the better offer?

1. Rs. 12,000 in cash
2. Rs. 12,880 at credit
3. Both are equally good

Answer: Rs. 12,000 in cash

The present value of Rs. 12,880 due after 8 months at 18% per annum is less than Rs. 12,000. Therefore, the cash offer is better.

Q8. If Rs. 10 be allowed as true discount on a bill of Rs. 110 due at the end of a certain time, then the discount allowed on the same sum due at the end of double the time is:

1. Rs. 20
2. Rs. 21.81
3. Rs. 22
4. Rs. 18.33

Answer: Rs. 18.33

From the first case, the present worth is Rs. 100 and the rate-time product can be found. Doubling the time changes the discount nonlinearly, and the new true discount comes to Rs. 18.33.

Q9. The banker's discount on a bill due 4 months hence at 15% is Rs. 420. The true discount is:

1. Rs. 400
2. Rs. 360
3. Rs. 480
4. Rs. 320

Answer: Rs. 400

Banker's discount is calculated on the face value, while true discount is calculated on the present worth. Using the standard relation between them for 4 months at 15%, the true discount is Rs. 400.

Q10. The banker's discount on Rs. 1600 at 15% per annum is the same as the true discount on Rs. 1680 for the same time and at the same rate. The time is:

1. 3 months
2. 4 months
3. 6 months
4. 8 months

Answer: 4 months

Let the time be t years. The banker's discount on Rs. 1600 is 1600×15×t/100, and the true discount on Rs. 1680 is found using the present worth formula. Equating them gives t = 1/3 year, i.e. 4 months.