# Arithmetic - Simple & Compound Interest - Previous Year CAT/MBA Questions

You can practice all previous year CAT questions from the topic Arithmetic - Simple & Compound Interest. This will help you understand the type of questions asked in CAT. It would be best if you clear your concepts before you practice previous year CAT questions.

**CAT 2022 QA Slot 1 | Arithmetic - Simple & Compound Interest**

Alex invested his savings in two parts. The simple interest earned on the first part at 15% per annum for 4 years is the same as the simple interest earned on the second part at 12% per annum for 3 years. Then, the percentage of his savings invested in the first part is

- A.
40%

- B.
62.5%

- C.
60%

- D.
37.5%

Answer: Option D

**Explanation** :

Let the amount invested in first and second parts is F and S respectively.

⇒ $\frac{\mathrm{F}\times 15\times 4}{100}$ = $\frac{\mathrm{S}\times 12\times 3}{100}$

⇒ $\frac{\mathrm{F}}{\mathrm{S}}$ = $\frac{3}{5}$

⇒ % amount invested in first part = $\frac{3}{3+5}$ × 100% = 37.5%

Hence, option (d).

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**CAT 2022 QA Slot 2 | Arithmetic - Simple & Compound Interest**

Mr. Pinto invests one-fifth of his capital at 6%, one-third at 10% and the remaining at 1%, each rate being simple interest per annum. Then, the minimum number of years required for the cumulative interest income from these investments to equal or exceed his initial capital is

Answer: 20

**Explanation** :

Let the total investment be Rs. 1500.

⇒ Rs. 300 is invested at 6% ⇒ Interest/year = Rs. 18

⇒ Rs. 500 is invested at 10% ⇒ Interest/year = Rs. 50

⇒ Rs. 700 is invested at 1% ⇒ Interest/year = Rs. 7

∴ Total interest received/year = 18 + 50 + 7 = Rs. 75

⇒ Time required to receive Rs. 1500 as interest = $\frac{1500}{75}$ = 20 years.

Hence, 20.

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**CAT 2022 QA Slot 3 | Arithmetic - Simple & Compound Interest**

Nitu has an initial capital of Rs. 20,000. Out of this, she invests Rs. 8,000 at 5.5% in bank A, Rs. 5,000 at 5.6% in bank B and the remaining amount at x% in bank C, each rate being simple interest per annum. Her combined annual interest income from these investments is equal to 5% of the initial capital. If she had invested her entire initial capital in bank C alone, then her annual interest income, in rupees, would have been

- A.
800

- B.
700

- C.
900

- D.
1000

Answer: Option A

**Explanation** :

Rs. 8000 is invested at 5.5% earning yearly interest of 8000 × 5.5% = Rs. 440

Rs. 5000 is invested at 5.6% earning yearly interest of 5000 × 5.6% = Rs. 280

Rs. 7000 is invested at x% earning yearly interest of 7000 × x% = Rs. 70x

Overall, 20,000 is invested which earns 5% yearly interest = 5% of 20000 = 1000

⇒ 440 + 280 + 70x = 1000

⇒ 70x = 1000 – 720 = 280

⇒ x = 4%

∴ If she had invested her entire initial capital in bank C alone, then her annual interest income = 4% of 20000 = Rs. 800

Hence, option (a).

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**CAT 2021 QA Slot 1 | Arithmetic - Simple & Compound Interest**

Anil invests some money at a fixed rate of interest, compounded annually. If the interests accrued during the second and third year are ₹ 806.25 and ₹ 866.72, respectively, the interest accrued, in INR, during the fourth year is nearest to

- A.
934.65

- B.
926.84

- C.
931.72

- D.
929.48

Answer: Option C

**Explanation** :

Let the interest accrued during first year = I and rate of interest be r%

We know in case of compound interest, interest for each year increases by r% every year.

∴ Interest for 2^{nd} year = I × $\left(1+\frac{r}{100}\right)$ = 806.25 …(1)

Interest for 3^{rd} year = I × ${\left(1+\frac{r}{100}\right)}^{2}$ = 866.72 …(2)

(2) ÷ (1)

⇒ $\left(1+\frac{r}{100}\right)$ = $\frac{866.72}{806.25}$ = 1 - $\frac{60.47}{806.25}$

⇒ r = 7.5%

∴ Interest for 4^{th} year = Interest for 3^{rd} year × (1+r/100)

= 866.72 × $\left(1+\frac{7.5}{100}\right)$ = 931.72

Hence, option (c).

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**CAT 2021 QA Slot 3 | Arithmetic - Simple & Compound Interest**

Bank A offers 6% interest rate per annum compounded half yearly. Bank B and Bank C offer simple interest but the annual interest rate offered by Bank C is twice that of Bank B. Raju invests a certain amount in Bank B for a certain period and Rupa invests ₹ 10,000 in Bank C for twice that period. The interest that would accrue to Raju during that period is equal to the interest that would have accrued had he invested the same amount in Bank A for one year. The interest accrued, in INR, to Rupa is

- A.
2346

- B.
3436

- C.
1436

- D.
2436

Answer: Option D

**Explanation** :

Let Raju invests Rs. A in bank B at r% p.a. for t years.

∴ Raju invests Rs. 10,000 in bank C at 2r% p.a. for 2t years.

Total interest accrued for Raju = Art/100

This is same as interest accrued by investing same amount in bank A for a year.

Amount due after 1 year in bank A = A${\left[1+\frac{3}{100}\right]}^{2}$ = 1.0609A

Interest accrued = 1.0609A - A = 0.0609A

⇒ 0.0609A = $\frac{Art}{100}$

⇒ rt = 6.09

Now, interest accrued by Rupa = $\frac{10000\times 2r\times 2t}{100}$ = 400 × rt = 400 × 6.09 = 2436.

Hence, option (d).

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**CAT 2020 QA Slot 1 | Arithmetic - Simple & Compound Interest**

Veeru invested Rs. 10,000 at 5% simple annual interest, and exactly after two years, Joy invested Rs. 8,000 at 10% simple annual interest. How many years after Veeru’s investment, will their balances, i.e., principal plus accumulated interest, be equal?

Answer: 12

**Explanation** :

Let the amounts become equal in t years.

Veeru’s investment after t years = 10000$\left(1+\frac{5\times t}{100}\right)$

Joy’s investment after t years = 8000$\left(1+\frac{10\times (t-2)}{100}\right)$

∴ 10000$\left(1+\frac{5\times t}{100}\right)$ = 8000$\left(1+\frac{10\times (t-2)}{100}\right)$

⇒ 5$\left(1+\frac{5\times t}{100}\right)$ = 4$\left(1+\frac{10\times (t-2)}{100}\right)$

⇒ 500 + 25t = 400 + 40t - 80

⇒ t = 12

Hence, 12.

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**CAT 2020 QA Slot 2 | Arithmetic - Simple & Compound Interest**

For the same principal amount, the compound interest for two years at 5% per annum exceeds the simple interest for three years at 3% per annum by Rs 1125. Then the principal amount in rupees is

Answer: 90000

**Explanation** :

Let the Principal be Rs. P.

Simple Interest for 3 years = $\frac{3\times P\times 3}{100}=\frac{9\mathrm{P}}{100}$ = 0.09P

Compound Interest for 2 years = P × 1.05^{2} – P = 0.1025P

∴ 0.1025P – 0.09P = 1125

⇒ 0.0125P = 1125

⇒ P = 90,000

Hence, 90000.

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**CAT 2020 QA Slot 3 | Arithmetic - Simple & Compound Interest**

A person invested a certain amount of money at 10% annual interest, compounded half-yearly. After one and a half years, the interest and principal together became Rs 18522. The amount, in rupees, that the person had invested is

Answer: 16000

**Explanation** :

Rate of interest is 10% per annum. Hence, interest for half a year is 5%.

The Principal, P is invested for 1.5 years or 3 terms of half years.

Therefore, P (1 + 5%)^{3} = 18522.

⇒ P × 1.05^{3} = 18522

⇒ P × ${\left(\frac{105}{100}\right)}^{3}$= 18522

⇒ P × ${\left(\frac{21}{20}\right)}^{3}$ = 2 × 213

⇒ P = 2 × 20^{3} = 16000.

Hence, 16000.

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**CAT 2019 QA Slot 1 | Arithmetic - Simple & Compound Interest**

Amala, Bina, and Gouri invest money in the ratio 3 : 4 : 5 in fixed deposits having respective annual interest rates in the ratio 6 : 5 : 4. What is their total interest income (in Rs) after a year, if Bina's interest income exceeds Amala's by Rs 250?

- A.
7000

- B.
7250

- C.
6350

- D.
6000

Answer: Option B

**Explanation** :

Let the amount invested by Amala, Bina and Gouri be 3x, 4x and 5x respectively.

Also, let the respective rates be 6r, 5r and 4r.

So, the respective ratio of simple interest is (3x × 6r) : (4x × 5r) : (5x × 4r) = 18xr : 20xr : 20xr.

Bina's interest income exceeds Amala's by Rs 250.

∴ 20xr − 18xr = 250.

∴ xr = 125.

Total interest income = 18xr + 20xr + 20xr = 58xr = 58 × 125 = Rs. 7250.

Hence, option (b).

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**CAT 2019 QA Slot 1 | Arithmetic - Simple & Compound Interest**

A person invested a total amount of Rs 15 lakh. A part of it was invested in a fixed deposit earning 6% annual interest, and the remaining amount was invested in two other deposits in the ratio 2 : 1, earning annual interest at the rates of 4% and 3%, respectively. If the total annual interest income is Rs 76,000 then the amount (in Rs lakh) invested in the fixed deposit was

Answer: 9

**Explanation** :

Since the amount invested is in the ratio 2 : 1, we can assum the amout to be 2x and x respectively.

∴ Amount invested in fixed deposit = 15L − 3x (where L is lakhs)

Simple interest earned on the fixed deposit = [(15L − 3x) × (6/100) × 1] ...(1)

Simple interest earned on 2x principle = 2x × (4/100) × 1 ...(2)

Simple interest earned on x principle = x × (3/100) × 1 ...(3)

(1) + (2) + (3) = 76000.

Solving we get; x = 2L.

So, amount invested in fixed deposit = 15L − 3x = 15L − 6L = 9L.

Hence, 9.

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**CAT 2019 QA Slot 2 | Arithmetic - Simple & Compound Interest**

Amal invests Rs 12000 at 8% interest, compounded annually, and Rs 10000 at 6% interest, compounded semi-annually, both investments being for one year. Bimal invests his money at 7.5% simple interest for one year. If Amal and Bimal get the same amount of interest, then the amount, in Rupees, invested by Bimal is

Answer: 20920

**Explanation** :

The amount on the first investment of Anmol = 12,000 × (1.08) = 12,960

So the Interest on this investment is 12,960 - 12,000 = 960.

The amount on the second investment of Anmol = 10,000 × (1.03)^{2} = 10,609

So the Interest on this investment is 10,609 - 10,000 = 609.

So the total interest on these returns = 960 + 609 = 1,569.

Bimal has to get this as Simple Interest by investing X rupees at 7.5%

That means, X × 0.075 = 1,569

X = 20,920

So, Bimal has to invest 20,920 rupees.

Hence, 20920.

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**CAT 2018 QA Slot 1 | Arithmetic - Simple & Compound Interest**

John borrowed Rs. 2,10,000 from a bank at an interest rate of 10% per annum, compounded annually. The loan was repaid in two equal instalments, the first after one year and the second after another year. The first instalment was interest of one year plus part of the principal amount, while the second was the rest of the principal amount plus due interest thereon. Then each instalment, in Rs., is

Answer: 121000

**Explanation** :

Let the part of principal amount in the first instalment be Rs. X.

Interest for the first year on Rs. 2,10,0000 = 210000 × 0.1 = 21,000

∴ The first instalment = (21000 + X)

Remaining part of the principal = (210000 – X)

Amount due on this principal of (210000 – X) = (210000 – X) × 1.1 = 231000 – 1.1X

∴ The second instalment = 231000 – 1.1X

∴ 21000 + X = 231000 – 1.1X

Solving this, we get X = 1,00,000

∴ Each instalment = 100000 + 21000 = Rs. 1,21,000

Hence, 121000.

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**CAT 2018 QA Slot 2 | Arithmetic - Simple & Compound Interest**

Gopal borrows Rs. X from Ankit at 8% annual interest. He then adds Rs. Y of his own money and lends Rs. X+Y to Ishan at 10% annual interest. At the end of the year, after returning Ankit’s dues, the net interest retained by Gopal is the same as that accrued to Ankit. On the other hand, had Gopal lent Rs. X+2Y to Ishan at 10%, then the net interest retained by him would have increased by Rs. 150. If all interests are compounded annually, then find the value of X + Y.

Answer: 4000

**Explanation** :

The only difference in the two situations is that in the second situation, Gopal lent Rs. Y more to Ishan than in the first situation. Therefore the additional interest retained by Gopal = 0.1Y.

Therefore 0.1.Y = 150 or Y = 1500.

Now, Ankit lent Gopal Rs. X at 8% interest. Therefore the interest retained by Ankit = Rs. 0.08X.

Gopal lent Ishan Rs. (X + 1500) at 10% interest.

Therefore the interest retained by Gopal = 0.1X + 150 - 0.08X = 0.02X + 150

Therefore, 0.08X = 0.02X + 1500 or X = 2500.

Therefore the value of X + Y = 4000.

Hence, 4000.

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**CAT 1995 QA | Arithmetic - Simple & Compound Interest**

A man invests Rs.3,000 at the rate of 5% per annum. How much more should he invest at the rate of 8%, so that he can earn a total of 6% per annum?

- A.
Rs. 1,200

- B.
Rs. 1,300

- C.
Rs. 1,500

- D.
Rs. 2,000

Answer: Option C

**Explanation** :

Using alligation, the ratio of the amounts invested at both the rates = 2 : 1.

Since he has invested Rs.3,000 at 5%, he should further invest Rs.1,500 at 8% to earn a total interest of 6% per annum.

**Alternative method:**

Let the amount invested at 8% be Rs. x.

Then, $3000\times \frac{105}{100}+x\times \frac{108}{100}=(3000+x)\frac{106}{100}$

⇒ 0.02x = 30 ⇒ x = 1,500

∴ He should further invest Rs.1,500 at 5% to earn a total interest of 6% per annum.

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**Read the following information and answer the questions that follows:**

Ghosh Babu deposited a certain sum of money in a bank in 1986. The bank calculated interest on the principal at 10 percent simple interest, and credited it to the account once a year. After the 1st year, Ghosh Babu withdrew the entire interest and 20% of the initial amount. After the 2nd year, he withdrew the interest and 50% of the remaining amount. After the 3rd year, he withdrew the interest and 50% of the remaining amount. Finally after the 4th year, Ghosh Babu closed the account and collected the entire balance of Rs. 11,000.

**CAT 1991 QA | Arithmetic - Simple & Compound Interest**

The initial amount in rupees, deposited by Ghosh Babu was:

- A.
25,000

- B.
75,000

- C.
50,000

- D.
None of these

Answer: Option C

**Explanation** :

Let us assume that Ghosh Babu had deposited Rs.100 initially.

Hence, had he deposited Rs.100 initially, he should have withdrawn Rs.22 at the end to close the account.

Since he withdrew Rs.11000, at the end, he should have initially deposited = 100/22 × 11,000 = Rs.50,000.

Hence, option (c).

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**CAT 1991 QA | Arithmetic - Simple & Compound Interest**

The year, at the end of which, Ghosh Babu withdrew the smallest amount was:

- A.
First

- B.
Second

- C.
Third

- D.
Fourth

Answer: Option D

**Explanation** :

Consider the solution for first question of this set.

He withdrew the smallest amount after the 4^{th} year.

Hence, option (d).

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**CAT 1991 QA | Arithmetic - Simple & Compound Interest**

The year, at the end of which, Ghosh Babu collected the maximum interest was:

- A.
First

- B.
Second

- C.
Third

- D.
Fourth

Answer: Option A

**Explanation** :

Consider the solution for first question of this set.

He collected the maximum interest after the 1^{st} year.

Hence, option (a).

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**CAT 1991 QA | Arithmetic - Simple & Compound Interest**

The year, at the end of which, Ghosh Babu withdrew the maximum amount was:

- A.
First

- B.
Second

- C.
Third

- D.
Fourth

Answer: Option B

**Explanation** :

Ghosh Babu withdrew the maximum amount after the 2nd year.

Hence, option (b).

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**CAT 1991 QA | Arithmetic - Simple & Compound Interest**

The total interest, in rupees, collected by Ghosh Babu was:

- A.
12,000

- B.
20,000

- C.
4,000

- D.
11,000

Answer: Option A

**Explanation** :

Consider the solution for first question of this set.

As seen from the table, the total interest collected by Ghosh Babu is Rs.24 on Rs.100.

Hence on Rs.50000, it would be 24/100 × Rs. 50,000 = Rs. 12,000

Hence, option (a).

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**CAT 1991 QA | Arithmetic - Simple & Compound Interest**

A sum of money compounded annually becomes Rs. 625 in two years and Rs. 675 in three years. The rate of interest per annum is

- A.
7%

- B.
8%

- C.
6%

- D.
5%

Answer: Option B

**Explanation** :

For a difference of 1 year, CI can be computed as SI.

Hence, from the 2nd year to the 3rd year interest earned = (675 – 625) = Rs. 50 on Rs. 625.

Hence the Rate of interest 50/625 × 100 = 8% p.a.

Hence, option (b).

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