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
231
What sum of money will amount to Rs. 520 in 5 years and to Rs. 568 in 7 years at simple interest?
Answer:
Rs. 400
The interest earned in 2 years (from year 5 to year 7) is 568 - 520 = Rs. 48. Simple interest for 1 year is 48 / 2 = Rs. 24. Interest for 5 years is 24 × 5 = Rs. 120. Since Amount = Principal + SI, the Principal = Amount in 5 years - SI for 5 years = 520 - 120 = Rs. 400.
232
A man invested 1/3 of his capital at 7%, 1/4 at 8%, and the remainder at 10%. If his annual income is Rs. 561, find the capital.
Answer:
Rs. 6600
Let the total capital be P. The remainder of the capital is 1 - (1/3 + 1/4) = 1 - 7/12 = 5/12. Total SI = (P/3 × 7/100) + (P/4 × 8/100) + (5P/12 × 10/100) = 561. This simplifies to 7P/300 + 8P/400 + 50P/1200 = 561. LCM is 1200. (28P + 24P + 50P) / 1200 = 561 => 102P = 561 × 1200 => P = Rs. 6600.
233
A sum of money doubles itself at compound interest in 15 years. In how many years will it become eight times?
Answer:
45 years
For compound interest, if a sum becomes 'x' times in 'T' years, it becomes x^n times in 'n × T' years. Here, it becomes 2 times in 15 years. We want to find when it becomes 8 times, which is 2³ times. So, n = 3. Time required = 3 × 15 = 45 years.
234
Find the principal if the difference between the compound interest and simple interest for 3 years at 10% per annum is Rs. 31.
Answer:
Rs. 1000
The formula for the difference between CI and SI for 3 years is D = P(R/100)²(3 + R/100). Plugging in the values: 31 = P(10/100)²(3 + 10/100) = P(1/100)(3.1). Therefore, 31 = P × 0.031. Solving for P gives P = 31 / 0.031 = Rs. 1000.
235
The compound interest on a certain sum for 2 years is Rs. 410 and the simple interest is Rs. 400. Find the rate of interest.
Answer:
5%
The SI for 2 years is Rs. 400, so SI for 1 year is Rs. 200. The difference between CI and SI for the second year is 410 - 400 = Rs. 10. This Rs. 10 is the interest earned on the first year's interest (Rs. 200). Rate = (10 / 200) × 100 = 5%.
236
In what time will Rs. 1000 become Rs. 1331 at 10% per annum compounded annually?
Answer:
3 years
Using the compound interest formula: 1331 = 1000(1 + 10/100)^T. This simplifies to 1331 / 1000 = (11/10)^T. Since 1331 is 11³ and 1000 is 10³, we get (11/10)³ = (11/10)^T. Therefore, T = 3 years.
237
A sum of Rs. 12000 amounts to Rs. 13230 in 2 years. Find the rate of compound interest per annum.
Answer:
5%
Using the formula A = P(1 + R/100)^T, we have 13230 = 12000(1 + R/100)². This gives (1 + R/100)² = 13230 / 12000 = 441 / 400. Taking the square root of both sides gives 1 + R/100 = 21/20. So, R/100 = 1/20, which means R = 5%.
238
What will be the compound interest on Rs. 8000 at 20% per annum for 9 months, compounded quarterly?
Answer:
Rs. 1261
When compounded quarterly, the rate is divided by 4, and time is multiplied by 4. Rate per quarter = 20% / 4 = 5%. Time = 9 months = 3 quarters. Amount A = 8000(1 + 5/100)³ = 8000(21/20)³ = 8000 × (9261 / 8000) = 9261. CI = 9261 - 8000 = Rs. 1261.
239
The difference between simple interest and compound interest on a sum of money for 2 years at 5% per annum is Rs. 15. Find the sum.
Answer:
Rs. 6000
The formula for the difference between CI and SI for 2 years is D = P(R/100)². Substituting the given values: 15 = P(5/100)². This simplifies to 15 = P(1/20)² = P/400. Therefore, P = 15 × 400 = Rs. 6000.
240
Calculate the compound interest on Rs. 10000 for 2 years at 10% per annum.
Answer:
Rs. 2100
Using the compound interest formula A = P(1 + R/100)^T, the Amount A = 10000(1 + 10/100)² = 10000(1.10)² = 10000 × 1.21 = Rs. 12100. The Compound Interest (CI) is Amount - Principal = 12100 - 10000 = Rs. 2100.