Mathematics/General Ability MCQs
Topic Notes: Mathematics/General Ability
MCQs and preparation resources for competitive exams, covering important concepts, past papers, and detailed explanations.
Plato
- Biography: Ancient Greek philosopher (427–347 BCE), student of Socrates and teacher of Aristotle, founder of the Academy in Athens.
- Important Ideas:
- Theory of Forms
- Philosopher-King
- Ideal State
221
The difference between simple and compound interest compounded annually on a certain sum of money for 2 years at 4% per annum is Rs. 1. The sum is:
Answer:
Rs. 625
The formula for the difference for 2 years is D = P(R/100)². Substituting the given values: 1 = P(4/100)² = P(1/25)² = P / 625. Therefore, Principal P = Rs. 625.
222
At what rate of compound interest per annum will a sum of Rs. 1200 become Rs. 1348.32 in 2 years?
Answer:
6%
Formula: A = P(1 + R/100)^T. 1348.32 = 1200(1 + R/100)². (1 + R/100)² = 1348.32 / 1200 = 1.1236. Taking the square root, 1 + R/100 = 1.06. This gives R/100 = 0.06, so R = 6%.
223
Find the compound interest on Rs. 5000 at 8% per annum for 1 year, compounded half-yearly.
Answer:
Rs. 408
For half-yearly compounding, the rate is halved to 4% per half-year, and time is doubled to 2 half-years. Amount = 5000(1 + 4/100)² = 5000(26/25)² = 5000 × 676 / 625 = 8 × 676 = Rs. 5408. Compound Interest = 5408 - 5000 = Rs. 408.
224
A sum was invested at simple interest for 2 years. Had it been invested at 3% higher rate, it would have yielded Rs. 300 more. What is the sum invested?
Answer:
Rs. 5000
The extra interest of Rs. 300 is due to the 3% higher rate over 2 years. Using the formula: Extra SI = (P × Extra Rate × Time) / 100. 300 = (P × 3 × 2) / 100. This gives 6P = 30000, which means P = Rs. 5000.
225
An amount is lent at simple interest. It grows to Rs. 1012 in 2.5 years and to Rs. 1067.20 in 4 years. What is the rate of interest?
Answer:
4%
Interest for 1.5 years (4 - 2.5) = 1067.20 - 1012 = Rs. 55.20. Interest for 1 year = 55.20 / 1.5 = Rs. 36.80. Interest for 2.5 years = 36.80 × 2.5 = Rs. 92. Principal = 1012 - 92 = Rs. 920. Rate = (36.80 × 100) / (920 × 1) = 4%.
226
If the compound interest on a sum for 2 years at 12.5% per annum is Rs. 510, the simple interest on the same sum at the same rate for the same period would be:
Answer:
Rs. 480
Let Principal be P. The rate is 12.5% = 1/8. Effective CI rate for 2 years = (1/8 + 1/8 + 1/64) = 17/64 of P. Given (17/64)P = 510, so P = (510 × 64) / 17 = 1920. SI for 2 years = (P × R × T) / 100 = (1920 × 12.5 × 2) / 100 = Rs. 480.
227
Find the compound interest on Rs. 16000 at 20% per annum for 9 months, compounded quarterly.
Answer:
Rs. 2522
Compounded quarterly means the rate R = 20% / 4 = 5% per quarter, and time n = 9 months = 3 quarters. Amount A = 16000(1 + 5/100)³ = 16000(21/20)³ = 16000 × 9261 / 8000 = 2 × 9261 = Rs. 18522. Compound Interest = 18522 - 16000 = Rs. 2522.
228
A sum was put at simple interest at a certain rate for 3 years. Had it been put at 2% higher rate, it would have fetched Rs. 360 more. Find the sum.
Answer:
Rs. 6000
The extra interest of Rs. 360 is generated purely by the extra 2% rate over 3 years. Let the principal be P. Extra SI = (P × Extra Rate × Time) / 100. 360 = (P × 2 × 3) / 100. This gives 6P = 36000, so P = Rs. 6000.
229
A lent Rs. 5000 to B for 2 years and Rs. 3000 to C for 4 years on simple interest at the same rate. He received Rs. 2200 in all from both as interest. The rate of interest is:
Answer:
10%
Total SI = SI from B + SI from C. 2200 = (5000 × R × 2) / 100 + (3000 × R × 4) / 100. This simplifies to 2200 = 100R + 120R = 220R. Therefore, R = 2200 / 220 = 10% per annum.
230
A sum of money amounts to Rs. 9800 after 5 years and Rs. 12005 after 8 years at the same rate of simple interest. The rate of interest per annum is:
Answer:
12%
Interest for 3 years (8 - 5) is 12005 - 9800 = Rs. 2205. Interest for 1 year = 2205 / 3 = Rs. 735. Interest for 5 years = 735 × 5 = Rs. 3675. Principal = 9800 - 3675 = Rs. 6125. The rate R = (SI × 100) / (P × T) = (735 × 100) / (6125 × 1) = 12%.