Simple and Compound Interest Questions

Multiple choice

Which information is/are sufficient to answer the questions asked? A sum of money is put at CI. Find the rate percent when the interest is reckoned yearly. I. The ratio of SI to CI at the end of 3 years on the same sum and same rate of interest is 300: 331. II. If the same sum is put at SI for 5 years on the same rate of interest then the SI will be 50% less than the principal amount. III. The difference between CI and SI at the end of 2 years on the same sum and same rate of interest is Rs 200. पूछे गए प्रश्नों का उत्तर देने के लिए कौन सी जानकारियाँ पर्याप्त हैं? एक धनराशि को चक्रवृद्धि ब्याज पर लगाया गया । दर प्रतिशत ज्ञात कीजिये यदि ब्याज वार्षिक रूप से नियोजित होता है। I. समान धनराशि पर 3 वर्षों के अंत में समान ब्याज दर से साधारण ब्याज का चक्रवृद्धि ब्याज से अनुपात 300: 331 है। II. यदि समान धनराशि और समान ब्याज की दर से 5 वर्ष के लिए साधारण ब्याज पर रखी जाती है तो साधारण ब्याज मूल धनराशि से 50% कम होगा। III. समान राशि और समान ब्याज की दर पर 2 साल के अंत में चक्रवृद्धि और साधारण ब्याज के बीच का अंतर 200 रुपए है ।

  1. Any two of them इनमें से कोई भी दो

  2. III and (I or II) III और (I या II)

  3. I or II alone is sufficient I या II अकेले पर्याप्त है

  4. II or (I and III) II या (I तथा III)

  5. None of these इनमें से कोई नहीं

Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Statement I gives the ratio SI:CI = 300:331 after 3 years. Using the compound interest formula A = P(1+r)^3, this ratio depends only on r, which we can solve for. Statement II says 5 years of SI equals 50% of principal, so 5Pr = 0.5P, giving r = 10% directly. Statement III gives one equation with two unknowns (P and r), so it's insufficient alone.

Multiple choice
  1. Rs.1820

  2. Rs.1758

  3. Rs.1785

  4. Rs.1930

  5. None of these इनमें से कोई नहीं

Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Interest paid by M to A = 1150 × 6 × 3/100 = Rs.207. Interest received by M from S on Rs.x at 9% for 3 years = x × 9 × 3/100 = 0.27x. M's gain = Interest received - Interest paid = 0.27x - 207 = 274.95. Solving: 0.27x = 481.95, x = 481.95/0.27 = Rs.1785. Option A (Rs.1820) would give a gain of Rs.285.30, Option B (Rs.1758) would give Rs.266.94, and Option D (Rs.1930) would give Rs.313.20.

Multiple choice
  1. 7500

  2. 8400

  3. 12000

  4. 9000

  5. 10000

Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let P be principal in Scheme A. After 12 years at 8% SI: Amount = P + (P × 8 × 12)/100 = P + 0.96P = 1.96P. This is invested in Scheme B at 20% CI for 2 years: Amount = 1.96P × (1.20)² = 1.96P × 1.44 = 2.8224P = 23708.16. So P = 23708.16 ÷ 2.8224 = 8400. Option B is correct.

Multiple choice
  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 लेकिन केवल कथन I नहीं

  3. If each statement alone (either I or II) is sufficient. यदि या केवल 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 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
D Correct answer
Explanation

Statement I gives final amount (Rs. 13331) but no principal or time. Statement II gives time (3 years) but no principal or final amount. Even together, we have two unknowns (principal P and rate R) with only one equation: P(1 + R/100)^3 = 1331. Multiple (P,R) pairs satisfy this, so rate cannot be uniquely determined. Neither statement nor both together are sufficient.

Multiple choice
  1. Any two कोई दो

  2. III and either I or II III और या तो I या II

  3. I and either II or III I और या तो II

  4. II and either I or III II और या तो I या III

  5. All सभी

Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

From I: Amount = 10000(1 + r/100)² = 11025, giving (1 + r/100)² = 1.1025, so 1 + r/100 = 1.05 or r = 5%. From II: Amount = 10000 + 10000×r×2/100 = 11000, giving 10000 + 200r = 11000 or r = 5%. From III: Principal = 10000. I alone gives rate (assuming standard principal). II alone gives rate (assuming standard principal). III alone is insufficient. With III, both I and II individually give the rate. Any two statements are sufficient - III with either I or II, or I and II together.

Multiple choice
  1. 6%

  2. 12%

  3. 15%

  4. 9%

  5. None of these इनमें से कोई नहीं

Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Let's verify: First loan of Rs.1500 at rate r% for 2 years gives interest = 1500 × r × 2 / 100 = 30r. Second loan of Rs.500 at 3r% for 6 months (from 18 months to 24 months) gives interest = 500 × 3r × 0.5 / 100 = 7.5r. Total interest = 30r + 7.5r = 37.5r = 262.50, so r = 7%. Since 7% is not among the given options, the correct answer is 'None of these'.

Multiple choice
  1. Quantity I > Quantity II मात्रा I > मात्रा II

  2. Quantity I ≥ Quantity II मात्रा I > मात्रा II

  3. Quantity II > Quantity I मात्रा II > मात्रा I

  4. Quantity II ≥ Quantity I मात्रा II > मात्रा I

  5. Quantity I = Quantity II or Relation cannot be established मात्रा I = मात्रा II या सम्बन्ध स्थापित नहीं किया जा सकता है

Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Quantity I: SI = P×R×T/100 = 6200×6×5/100 = 6200×30/100 = 1860. Quantity II: CI compounded semi-annually means rate=10/2=5% per half-year, time=2 periods. CI = 6400×(1.05)² - 6400 = 6400×1.1025 - 6400 = 7056 - 6400 = 656. Since 1860 > 656, Quantity I > Quantity II.

Multiple choice
  1. Quantity I > Quantity II मात्रा I > मात्रा II

  2. Quantity I ≥ Quantity II मात्रा I ≥ मात्रा II

  3. Quantity II > Quantity I मात्रा II > मात्रा I

  4. Quantity II ≥ Quantity I मात्रा II ≥ मात्रा I

  5. Quantity I = Quantity II or Relation cannot be established मात्रा I = मात्रा II या संबंध स्थापित नहीं किया जा सकता है

Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Quantity I: Compound interest on ₹10000 at 20% for 2 years. Year 1: ₹10000 + 20% = ₹12000. Year 2: ₹12000 + 20% = ₹14400. Quantity II: Simple interest on ₹9000 at 15% for 4 years. Interest = 9000 × 15% × 4 = ₹5400. Amount = ₹9000 + ₹5400 = ₹14400. Both quantities equal ₹14400, so relationship cannot be established (they are equal).

Multiple choice
  1. Quantity I > Quantity II मात्रा I > मात्रा II

  2. Quantity I ≥ Quantity II मात्रा I > मात्रा II

  3. Quantity II > Quantity I मात्रा II > मात्रा

  4. Quantity II ≥ Quantity I मात्रा II > मात्रा

  5. Quantity I = Quantity II or Relation cannot be established मात्रा I = मात्रा II या सम्बन्ध स्थापित नहीं किया जा सकता है ।

Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Quantity I: SI = P × R × T / 100 = 12000 × 10 × 2 / 100 = Rs. 2400. Quantity II: CI is compounded semi-annually, so rate = 5% per half-year for 3 periods. CI = 12000(1 + 5/100)³ - 12000 = 12000 × 1.157625 - 12000 ≈ Rs. 1891. Since 2400 > 1891, Quantity I > Quantity II.

Multiple choice

Each of these questions consists of a question followed by informations in three statements. You have to study the question and the statements and decide that information in which of the statement(s) is/are necessary to answer the question. नीचे प्रत्येक प्रश्न में, एक प्रश्न और उसके बाद तीन कथनों में जानकारी दी गई है। आप प्रश्न और कथनों का अध्ययन कीजिए और यह तय कीजिये कि कौनसा/से कथनों में दी गई जानकारी प्रश्न का उत्तर देने के लिए आवश्यक है/हैं। Find the amount at the end of 3 years and 6 months- 3 वर्ष और 6 माह के अंत में मिश्रधन ज्ञात कीजिये - Statement I: If a principal is invested at same rate of simple interest for 3 years it becomes 3 times. Statement II: The principal produces a compound interest of 1700 if invested at same rate of interest for 2 years. Statement III: Any principal invested at same rate of compound interest become 126.5625% at the end of 2 years. कथन I: यदि एक मूलधन 3 वर्ष के लिए साधारण ब्याज दर पर निवेश करता है तो यह 3 गुना हो जाता है। कथन II: यदि मूलधन को 2 वर्षों के लिए समान चक्रवृद्धि ब्याज दर निवेश किया जाता है तो 1700 का चक्रवृद्धि ब्याज प्राप्त होता है। कथन III: यदि मूलधन को 2 वर्षो के लिए चक्रवृद्धि ब्याज पर निवेश किया जाता है तो यह खुद का 126.5625% हो जाता है।

  1. I and either II or III I तथा II या III

  2. Any two कोई भी दो

  3. II and either I or III कोई भी दो

  4. II and III II तथा III

  5. None of these इनमे से कोई नहीं

Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

From Statement III: (1+r)^2 = 126.5625/100 = 1.265625, so 1+r = 1.125, giving r = 12.5%. From Statement II: CI = P((1.125)^2 - 1) = 1700, so P = 1700/0.265625 = 6400. Amount at 3.5 years = 6400(1.125)^3.5 ≈ 9431. Statements II and III together give both rate and principal. While Statements I and III give different rates, Option C specifies the valid combination.

Multiple choice
  1. Quantity I < Quantity II मात्राI < मात्राII

  2. Quantity I ≤ Quantity II मात्रा I ≤ मात्रा II

  3. Quantity I > Quantity II मात्रा I > मात्रा II

  4. Quantity I ≥ Quantity II मात्रा I ≥ मात्रा II

  5. Quantity I = Quantity II or Relation cannot be establish मात्रा I = मात्रा II या सम्बंध स्थापित नही किया जा सकता है |

Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For Quantity I: Difference between CI and SI for 2 years = P*(r/100)^2. So 320 = 32000*(r/100)^2, giving (r/100)^2 = 1/100, therefore r = 10%. For Quantity II: Amount triples in 14 years at SI, so 2P = P*r*14/100, giving r = 200/14 = 14.29%. Since 10% < 14.29%, Quantity I < Quantity II.

Multiple choice
  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: Interest = 33.1% of principal, so z = x + 0.331x = 1.331x = x : z = 1 : 1.331. This is sufficient alone. Statement C: CI at 10% for 3 years gives amount = x(1.1)³ = 1.331x, so x : z = 1 : 1.331. This is also sufficient alone. Statement A alone insufficient (only gives SI, not final amount). So either B or C alone works - answer B is correct.

Multiple choice
  1. Any two

  2. I and II

  3. I and II or III

  4. Only I

  5. None of these

Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let principal = P. Interest for 6 months at 10% = 5% of P. After tax at 4%, net interest = 5% × 96% = 4.8%. Annual interest = 2 × 4.8%P - 4.8%P × 4% = 9.6%P - 0.192%P = 9.408%P. Given 9.408%P = 1500, P = 1500/0.09408 ≈ Rs 15,947. Statement I gives interest amount, II gives compounding frequency, and the tax rate. Statement III is not needed. I and II together are sufficient.

Multiple choice
  1. All the statements are required to answer the question.

  2. Any two statements are sufficient to answer the question.

  3. Either statement I or II and statement III are required to answer the question.

  4. Statement I and III together are sufficient to answer the question.

  5. Statement II and III together are sufficient to answer the question.

Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement I provides the principal (Rs. 7000) and rate (5% per annum). Statement III tells us after 3 years he paid Rs. 3000 and cleared dues after 2 more years. Using I and III together: After 3 years, amount due = 7000 + (7000 × 0.05 × 3) = Rs. 8050. After paying Rs. 3000, remaining principal is Rs. 5050. This accumulates interest for 2 more years: 5050 × 0.05 × 2 = Rs. 505. Total paid = 3000 + 5050 + 505 = Rs. 8555. Statement II alone is insufficient as it only tells us he wants to repay in installments without specifics.

Multiple choice
  1. 2 years 2 वर्ष

  2. 7 years 7 वर्ष

  3. 4 years 4 वर्ष

  4. 5 years 5 वर्ष

  5. 8 years 8 वर्ष

Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For CI at 10% for 2 years, amount factor = 1.1² = 1.21. CI = P(1.21 - 1) = 0.21P = 1050, so P = 1050/0.21 = Rs. 5000. For SI at 8%, SI = P × 8 × T / 100 = 5000 × 8 × T / 100 = 400T = 2000. Thus T = 2000/400 = 5 years.