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
211
Compound interest on a certain sum for 2 years at 10% per annum is Rs. 420. Find the simple interest on the same sum at the same rate and for the same time.
Answer:
Rs. 400
The effective CI rate for 2 years at 10% is 10 + 10 + (10×10)/100 = 21%. Effective SI rate for 2 years is 20%. Since 21% of Principal = 420, Principal = (420 / 21) × 100 = 2000. SI = 20% of 2000 = Rs. 400.
212
The difference between the simple interest received from two different sources on Rs. 1500 for 3 years is Rs. 13.50. The difference between their rates of interest is:
Answer:
0.3%
Let the two rates be R1 and R2. Difference in SI = [1500 × R1 × 3 / 100] - [1500 × R2 × 3 / 100] = 45(R1 - R2). Given that this difference is 13.50. Therefore, 45(R1 - R2) = 13.50, which gives R1 - R2 = 13.50 / 45 = 0.3%.
213
A sum of Rs. 1550 is lent out in two parts, one at 8% and another at 6%. If the total annual income is Rs. 106, find the money lent at 8%.
Answer:
Rs. 650
Let the sum lent at 8% be x. The remaining sum is (1550 - x). SI from first part = (x × 8 × 1)/100 = 0.08x. SI from second part = ((1550 - x) × 6 × 1)/100 = 93 - 0.06x. Total SI = 0.08x + 93 - 0.06x = 106. Solving gives 0.02x = 13, so x = 13 / 0.02 = Rs. 650.
214
What will be the ratio of simple interest earned by a certain amount at the same rate of interest for 6 years and that for 9 years?
Answer:
2:3
Simple interest is directly proportional to time when the principal and rate are constant. Therefore, the ratio of simple interests is equal to the ratio of their respective times: 6 years : 9 years = 6/9 = 2:3.
215
If a sum of money at simple interest doubles in 12 years, the rate of interest per annum is:
Answer:
8.33%
If a sum doubles, the simple interest earned equals the principal (SI = P). Using the formula R = (SI × 100) / (P × T), we get R = (P × 100) / (P × 12) = 100 / 12 = 8.33% per annum.
216
Rs. 800 amounts to Rs. 920 in 3 years at simple interest. If the interest rate is increased by 3%, it would amount to how much?
Answer:
Rs. 992
An increase of 3% in rate for 3 years generates an extra interest of 3% × 3 = 9% of the principal. Extra interest = 9% of 800 = Rs. 72. The new amount will be the original amount plus this extra interest: 920 + 72 = Rs. 992.
217
What is the simple interest on Rs. 3000 for 146 days at 5% per annum?
Answer:
Rs. 60
Convert days into years: Time = 146 / 365 = 2/5 years. SI = (P × R × T) / 100 = (3000 × 5 × 2/5) / 100. The 5s cancel out, giving SI = (3000 × 2) / 100 = 6000 / 100 = Rs. 60.
218
Simple interest on a certain sum is 16/25 of the sum. Find the rate percent and time if both are numerically equal.
Answer:
8% and 8 years
Let Principal be P. SI = (16/25)P. Let Rate R = Time T = x. Using the formula SI = (P × R × T)/100, we get (16/25)P = (P × x × x)/100. Simplifying this gives x² = (16 × 100) / 25 = 1600 / 25 = 64. Therefore, x = 8. So, rate is 8% and time is 8 years.
219
A certain sum amounts to Rs. 5832 in 2 years at 8% per annum compound interest. Find the sum.
Answer:
Rs. 5000
Amount A = P(1 + R/100)^T. 5832 = P(1 + 8/100)² = P(1.08)². 5832 = P × 1.1664. Solving for P gives P = 5832 / 1.1664 = Rs. 5000.
220
If a certain sum of money becomes 8 times of itself in 3 years at compound interest, find the rate of interest.
Answer:
100%
Let Principal be P and Amount be 8P. Using the formula A = P(1 + R/100)^T, we get 8P = P(1 + R/100)³. Dividing by P gives 8 = (1 + R/100)³. Since 8 is 2³, 2 = 1 + R/100. Thus, R/100 = 1, meaning R = 100%.