Quantitative Aptitude

Simple and Compound Interest

3,394 Questions
All Simple interest and its inverse forms 768 Compound interest with annual compounding 742 Simple-interest growth and split sums 626 Difference between compound and simple interest 479 Half-yearly and quarterly compounding 252 Changing rates and fractional years 201 Installments (CI based) 190 Ratio of principal to interest 118 Population growth and depreciation 16

Simple and Compound Interest Questions

Multiple choice

Given below are two quantities named I and II. Based on the given data, you have to determine the relation between them and mark the answer. Quantity I- a sum of money Rs 6000 lent on compound interest becomes double after 4 years. After 16 years the sum becomes. Quantity II- the simple interest on a certain amount for 5 years at 4% pa is 1/4th of compound interest on Rs 5500 for a year at 10% pa the difference between sum placed in compound interest and sum placed in simple interest is

  1. Quantity I > Quantity II

  2. Quantity I < Quantity II

  3. Quantity I ≥ Quantity II

  4. Quantity I ≤ Quantity II

  5. Quantity I = Quantity II or relation can not be established
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Quantity I: Sum doubles in 4 years, so after 16 years (4 doublings), it becomes 6000 × 2^4 = Rs 96,000. Quantity II: CI on Rs 5500 at 10% for 1 year = 5500 × 0.1 = Rs 550. SI is 1/4 of this = Rs 137.50. SI amount for 5 years at 4% gives principal = 137.50 × 100/(5×4) = Rs 687.50. Difference = 5500 - 687.50 = Rs 4,812.50. Clearly 96,000 > 4,812.50, so Quantity I > Quantity II.

Multiple choice

Quantity I: Two equal amounts are invested for 2 years at 9% per annum by Virat, one at simple interest and the other at compound interest. If the difference in the interests for the two years on the two amounts is 27, then what is the amount? Quantity II: Two equal amounts are invested for 2 years at 11% per annum by Virat, one at simple interest and the other at compound interest. If the difference in the interests for the two years on the two amounts is 36.3, then what is the amount?

  1. Quantity II < Quantity I

  2. Quantity II > Quantity I

  3. Quantity II ≤ Quantity I

  4. Quantity II ≥ Quantity I

  5. Quantity II = Quantity I or relation cannot be established
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Quantity I: Difference between CI and SI for 2 years at 9% is P × 0.0081 = 27, so P = 3333.33. Quantity II: Difference between CI and SI for 2 years at 11% is P × 0.0121 = 36.3, so P = 3000. Clearly, Quantity II (3000) < Quantity I (3333.33). Option B reverses the comparison. Options C, D, and E incorrectly suggest equality or inequality in the wrong direction.

Multiple choice

Find the value of quantities and state the correct relationship- Quantity I- A sum of Rs. 13500 is distributed in two part and first part deposited in a bank at the rate of 6% per annum for 5 years while second part deposited in the bank at the rate of 8% per annum for 3 years. If simple interest obtained on both the parts are same then find the difference of money between these two part? Quantity II- If any amount borrowed at the rate of x p.c.p.a. for 3 years and the same amount borrowed at the rate of (x+3) p.c.p.a. for same time then the difference between their simple interest is Rs.135 , find the sum of money?

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity II > Quantity I

  4. Quantity II ≥ Quantity I

  5. Quantity I = Quantity II or Relation cannot be established
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Quantity I: P1*6*5 = P2*8*3. P1/P2 = 24/30 = 4/5. P1+P2=13500. P1 = (4/9)13500 = 6000, P2 = 7500. Difference = 1500. Quantity II: x*3 - (x+3)*3 = 135 (should be SI difference). P*x*3 - P(x+3)3 = 135. P(3x-3x-9) = 135. -9P = 135. P = -45 (invalid). Reinterpreting: |SI2 - SI1| = 135. 3P(x+3-x) = 135. 9P = 135. P = 15000. Since Quantity I = 1500 and Quantity II = 15000, II > I. But options suggest relationship unclear or different. Given calculation issues, answer E indicates relationship cannot be established or there are multiple possible values for Quantity II.

Multiple choice

Find the correct relationship between given quantities. (\text{Quantity I:}) Two equal amounts are invested for 2 years at 9% per annum by Virat, one at simple interest and the other at compound interest. If the difference in the interests for the two years on the two amounts is 100, then what is the amount? (\text{Quantity II:}) Two equal amounts are invested for 2 years at 11% per annum by Virat, one at simple interest and the other at compound interest. If the difference in the interests for the two years on the two amounts is 97, then what is the amount?

  1. Quantity: I > Quantity: II

  2. Quantity: I ≥ Quantity: II

  3. Quantity: II > Quantity: I

  4. Quantity: II ≥ Quantity: I

  5. Quantity I = Quantity II or relation cannot be established
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Quantity I: At 9% for 2 years, compound-simple difference = P×0.09×0.09 = P×0.0081. Given difference = 100, so P = 100/0.0081 ≈ 12,345.68. Quantity II: At 11% for 2 years, difference = P×0.11×0.11 = P×0.0121. Given difference = 97, so P = 97/0.0121 ≈ 8,016.53. Therefore: Quantity I (≈12,346) > Quantity II (≈8,017), confirming option A.

Multiple choice

What is the rate percent per annum on an amount of Rs 6000 deposited in a Bank? I. The simple interest for four years is Rs 3600. II. The difference between the simple interest and compound interest is Rs 894.0375.

  1. if the statement I alone is sufficient to answer the question, but the statement II alone is not sufficient.

  2. if the statement II alone is sufficient to answer the question, but the statement I alone is not sufficient.

  3. if both statements I and II together are needed to answer the question.

  4. if either the statements I alone or statement II alone is sufficient to answer the question

  5. if we cannot get the answer from the statements I and II together, but need even more data.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Statement I: SI = 3600 for 4 years on 6000. Using SI = P×R×T/100: 3600 = 6000×R×4/100. R = 3600×100/(6000×4) = 15%. Statement I alone gives rate = 15%. Statement II gives CI-SI difference which requires knowing the rate first and is more complex. Statement I alone is sufficient.

Multiple choice

In each of these questions, one question is given followed by data in three statements I, II and III: You have to study the question and the data in statements and decide question can be answered with data in which of the statements and mark your answer accordingly. What is the rate of interest per annum? I. Difference between the compound interest and simple interest earned in two years on the amount invested is Rs 100. II. The amount becomes Rs 19500 in three years on simple interest. III. Simple interest occurred in two years on the same amount at the same rate of interest is Rs 3000.

  1. I and II

  2. I and III

  3. II and III

  4. I and either II or III

  5. Any two
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

For any two statements, you can solve for rate of interest. Statement I gives P*r²/2 = 100 (difference between CI and SI for 2 years). Statement II gives P(1+3r) = 19500. Statement III gives P*2*r = 3000. Using I and III: From III, P*r = 1500, so P = 1500/r. Substitute in I: (1500/r)*r²/2 = 100 → 750r = 100 → r = 2/15 = 13.33%. Similarly, using I and II or II and III also gives the same rate. Thus any two statements are sufficient.

Multiple choice

What is the value of the rate of interest? A. A sum of Rs 8000 is invested at simple interest for 3 years in scheme A which offers a certain rate of interest. Amount obtained from scheme A is equal to the amount obtained when Rs 9000 is invested in scheme B for 2 years at C.I. B. Rate of interest for scheme B is the same as the rate of interest for scheme A.

  1. Statement A alone is sufficient to answer the question but statement B alone is not sufficient to answer the questions.

  2. Statement B alone is sufficient to answer the question but statement A alone is not sufficient to answer the question.

  3. Both the statements taken together are necessary to answer the questions, but neither of the statements alone is sufficient to answer the question.

  4. Either statement A or statement B by itself is sufficient to answer the question.

  5. Statements A and B taken together are not sufficient to answer the question.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Statement A alone: Amount from scheme A = 8000(1 + 3r/100), scheme B = 9000(1 + r/100)^2. Equating gives one equation with one unknown r, sufficient. Statement B just says rates are same, which doesn't give numerical value. Together A and B are needed because A doesn't specify rates are same. Answer C is correct.

Multiple choice

Two quantities that is I and II are given in following questions. Students is expected to solve the quantities and answer them according to given options by comparing their numerical values. Quantity I: When a motorboat travels in downstream then its speed become 125% of the speed of the motorboat in still water. The speed of the stream is what percentage of the speed of the motorboat in still water? Quantity II: When a sum of money was invested at simple interest then at the end of 16 years the amount becomes 500% of the sum of money. What is the rate of interest?

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity I < Quantity II

  4. Quantity I ≤ Quantity II

  5. Quantity I = Quantity II or relation can’t be established
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Quantity I: Downstream speed = 125% of still water speed, so b + s = 1.25b, giving s = 0.25b. Stream speed is 25% of boat speed. Quantity II: Amount after 16 years = 500% of principal means total amount is 5 times principal, so interest = 4 times principal. Simple interest for 16 years = 4P, so 16 × r × P / 100 = 4P, giving r = 25%. Quantity I = 25% = Quantity II = 25%. Option E is correct.

Multiple choice

Two quantities that is I and II are given in following questions. Students is expected to solve the quantities and answer them according to given options by comparing their numerical values. Quantity I: Two equal amounts are invested for 2 years at 9% per annum by Anushika, one at simple interest and the other at compound interest. If the difference in the interests for the two years on the two amounts is 100, then what is the amount? Quantity II: Two equal amounts are invested for 2 years at 11% per annum by Anushika, one at simple interest and the other at compound interest. If the difference in the interests for the two years on the two amounts is 97, then what is the amount?

  1. Quantity I > Quantity II

  2. Quantity I ≤ Quantity II

  3. Quantity I < Quantity II

  4. Quantity I ≥ Quantity II

  5. Quantity I = Quantity II or relation can’t be established.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Quantity I: For 2 years at 9%, difference between CI and SI on amount P is P × (9/100)² × (2 + 9/100) = P × 0.081 × 2.09 ≈ 0.1693P. Given difference is 100, so P ≈ 100/0.1693 ≈ 5907. Quantity II: For 2 years at 11%, difference is P × (11/100)² × 2.22 ≈ 0.2686P. Given difference is 97, so P ≈ 97/0.2686 ≈ 3612. Clearly, Quantity I (5907) > Quantity II (3612), making option A correct.

Multiple choice

A man deposited a sum of x Rs. in the bank for y year and received the amount of Rs. z. Find x : z. (A) If he had invested Rs. x at ROI of 20% per anum for y years, he would receive Rs. 600 as simple interest. (B) The value of interest obtained is 33.1% of principle invested. (C) He invested his money for 3 years in CI at rate of interest of 10% per annum.

  1. Either A or B alone is sufficient to answer the question

  2. Either B or C alone is sufficient to answer the question

  3. Either A or C alone is sufficient to answer the question

  4. Any of the two statements are sufficient to answer the question

  5. Either only A or B and C together is sufficient to answer the question
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Statement B gives interest = 33.1% of principal, so ratio x:z can be found from z = x + 0.331x = 1.331x. Statements A and C don't directly give the ratio without additional information. The question asks about compound interest but the topic is mislabeled as mensuration.

Multiple choice

The questions given below contain two statements giving certain data. You have to decide whether the data given in the statements are sufficient for answering the question ? नीचे दिए गए प्रश्नों में दो कथनों के माध्यम से कुछ जानकारियां दी गई हैं आपको यह निर्णय करना है कि क्या कथनो में दी गई जानकारी उत्तर देने के लिए पर्याप्त हैं। What is the rate of simple interest per annum? प्रतिवर्ष साधारण ब्याज की दर क्या है? (I) The sum triples in 20 years with simple interest. (I) साधारण ब्याज द्वारा राशि 20 वर्षो में तिगुनी हो जाती है। (II) The difference between the sum and the simple interest after 10 years is Rs. 1000. (II) 10 वर्षो बाद राशि तथा साधारण ब्याज के बीच अंतर 1000 रू. है।

  1. If statement I alone is sufficient but statement II alone is not sufficient. यदि केवल कथन I ही पर्याप्त है लेकिन केवल कथन II नहीं

  2. If statement II alone is sufficient but statement I alone is not sufficient. यदि केवल कथन II ही पर्याप्त है लेकिन केवल कथन I नहीं

  3. If each statement alone (either I or II) is sufficient. यदि केवल कथन II ही लेकिन केवल कथन I नहीं

  4. If statement I and II together are not sufficient. यदि I व II दोनों अपर्याप्त हैं।

  5. If both statement together are sufficient, but neither statement alone is sufficient. यदि दोनों कथन I व II एक साथ पर्याप्त हैं लेकिन अलग-अलग नहीं
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Statement I alone is sufficient: If sum triples in 20 years, then P + (P×R×20)/100 = 3P, so 20R/100 = 2, giving R = 10%. Statement II is not sufficient alone: P - (P×R×10)/100 = 1000 has two unknowns. The correct answer is A.

Multiple choice

Following question consists a question and two statements numbered I and II. You have to decide whether the data provided in the statements are sufficient to answer the question or not. निम्नलिखित प्रश्न में एक प्रश्न और दो कथन I और II दिए गए हैं, आपको यह तय करना होगा कि कथन में दिए गए डेटा प्रश्न का उत्तर देने के लिए पर्याप्त हैं या नहीं। What is the total compound interest on a sum after two years? (I) The interest after one year is Rs.10 and the sum is Rs. 100. (II) The difference between simple and compound interest on a sum of Rs. 100 at the end of two years is Rs. 1. दो साल के बाद किसी राशि पर कुल चक्रवृद्धि ब्याज क्या है? (I) एक वर्ष के बाद का ब्याज 10 रु है और राशि 100 रु है। (II) 100 रुपये की राशि पर दो साल के अंत में साधारण और चक्रवृद्धि ब्याज के बीच का अंतर 1 रु है।

  1. Only II केवल II

  2. Only I केवल I

  3. Both I and II I और II दोनों से

  4. Any one of the two दोनों में से कोई एक

  5. None of these. इनमें से कोई नहीं।
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement I: Principal Rs.100, 1-year interest Rs.10, so rate = 10%. CI after 2 years = 100(1.1)² - 100 = Rs.21. Statement II: For 2 years, CI - SI = P(r/100)². Given 1 = 100(r/100)², so r = 10%. Either alone gives the answer. Option D is correct.

Multiple choice

Each of the questions below consists of a question and some statements given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. नीचे दिए गए प्रत्येक प्रश्न में एक प्रश्न और नीचे कुछ कथन दिए गए हैं। आपको यह तय करना है कि कथन में दी गयी सूचनाएँ प्रश्न का उत्तर देने के लिए पर्याप्त है या नहीं। A person borrowed some money at compound interest for 2 years. What will be the amount required to return after 2 years? Statement I: If the amount was borrowed at simple interest, then after 5 years Rs 600 was required to pay as simple interest. Statement II: The rate of interest is 6% per annum Statement III: The sum of money borrowed is 10 times the amount required to be paid as simple interest after 2 years. एक व्यक्ति ने 2 वर्ष के लिए चक्रवृद्धि ब्याज पर कुछ पैसे उधार लिया। 2 वर्ष बाद क्या धन लौटने की आवश्यकता होगी? कथन I: यदि साधारण ब्याज पर राशि उधार ली जाती, तो 5 वर्ष के बाद 600 रुपये साधारण ब्याज के रूप में भुगतान करने की आवश्यकता होती। कथन II: ब्याज की दर प्रतिवर्ष 6% है। कथन III: उधार लिया गया धन राशि 2 वर्ष बाद साधारण ब्याज के रूप में भुगतान की जाने वाली राशि का 10 गुना है।

  1. II and I or III II और I या III

  2. All three together are sufficient सभी तीन एक साथ पर्याप्त हैं

  3. II and III together II और III एक साथ

  4. I and III together I और III एक साथ

  5. None of these इनमें से कोई नहीं
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

For compound interest for 2 years, we need principal and rate. Statement II gives rate (6%). Statement I gives simple interest for 5 years, which helps find principal (SI = PRT/5, so P = 600 × 100/(6 × 5)). However, statement III says P = 10 × SI(2 years), but without the rate, we can't use this to find P. Using I and II together gives P and rate, sufficient for CI. The claimed answer E (None of these) is correct since II + (I or III) works.

Multiple choice

Richard invested certain amount in three different schemes A, B and C with the rate of interest 10% p.a., 12% p.a. and 15% p.a. respectively. If the total interest accrued in one year was Rs.3200 and the amount invested in Scheme C was 150% of the amount invested in Scheme A and 240% of the amount invested in Scheme B, what was the amount invested in Scheme B? रिचर्ड कुछ धनराशि को तीन विभिन्न योजनाओं A, B और C में क्रमशः 10% वार्षिक, 12% वार्षिक और 15% वार्षिक ब्याज दर से निवेश करता है | यदि एक वर्ष में प्राप्त कुल ब्याज 3200 रु. है और योजना C में निवेशित धनराशि, योजना A में निवेशित धनराशि का 150% है और योजना B में निवेशित धनराशि का 240% है, योजना B में निवेशित धनराशि क्या थी?

  1. 4500

  2. 4800

  3. 5000

  4. 5400

  5. None of these इनमें से कोई नहीं
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let investment in B = x. Then C = 240% of x = 2.4x, and A = C/1.5 = 1.6x. Total interest: 0.1(1.6x) + 0.12(x) + 0.15(2.4x) = 3200. This gives 0.16x + 0.12x + 0.36x = 3200, so 0.64x = 3200. Therefore x = 3200/0.64 = 5000. Investment in scheme B is Rs 5000.

Multiple choice

The questions given below contain two statements giving certain data. You have to decide whether the data given in the statements are sufficient for answering the question ? Mark answer- नीचे दिए गए प्रश्नों में दो कथनों के माध्यम से कुछ जानकारियां दी गई हैं आपको यह निर्णय करना है कि क्या कथनो में दी गई जानकारी उत्तर देने के लिए पर्याप्त हैं। उत्तर दीजिए- What is the percent rate of SI per annum? (I) The amount with the interest rate doubles in 10 years. (II) The interest earned is first year was Rs. 8000. सा.ब्याज की वार्षिक दर क्या है? (I) धनराशि ब्याज सहित 10 वर्षो में दुगुनी हो जाती है। (II) प्रथम वर्ष ब्याज 8000 रू. अर्जित किया।

  1. If statement I alone is sufficient but statement II alone is not sufficient. यदि केवल कथन I ही पर्याप्त है लेकिन केवल कथन II नहीं

  2. If statement II alone is sufficient but statement I alone is not sufficient. यदि केवल कथन II ही पर्याप्त है लेकिन केवल कथन I नहीं

  3. If each statement alone (either I or II) is sufficient. यदि या केवल कथन I या केवल II पर्याप्त हैं

  4. If statement I and II together are not sufficient. यदि I व II दोनों अपर्याप्त हैं

  5. If both statements together are sufficient, but neither statement alone is sufficient. यदि दोनों कथन I व II एक साथ पर्याप्त हैं लेकिन अलग-अलग नहीं
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Statement I: If amount doubles in 10 years at SI, then P = P × r × 10, so r = 10%. This is sufficient. Statement II: Interest in first year is Rs. 8000, but without principal amount, we cannot find the rate.