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
141
The difference between simple interest and compound interest on Rs. 4000 for 2 years at 10% per annum is:
Answer:
Rs. 40
Difference for 2 years = P(R/100)² = 4000(10/100)² = 4000(1/100) = Rs. 40.
142
The compound interest on Rs. 1000 for 2 years at 10% per annum compounded half-yearly is:
Answer:
Rs. 215.50
Rate per half year = 5%. Time = 4 periods. Amount = 1000(1.05)⁴ = 1000 × 1.215506 = 1215.50. CI = 1215.50 - 1000 = Rs. 215.50.
143
A tree increases annually by 1/8th of its height. By how much will it increase after 2.5 years, if it stands today 8 m high?
Answer:
10.75 m
Rate = 1/8 = 12.5%. For 2.5 years, Amount = P(1 + R/100)² × (1 + (R/2)/100). Height = 8(1 + 1/8)²(1 + 1/16) = 8 × (9/8) × (9/8) × (17/16) = 8 × (81/64) × (17/16) = 10.7578. The exact formula typically approximates for fractional years or takes exact: 8*(9/8)*(9/8) for 2 years = 10.125. For 0.5 year, simple interest on 10.125 = 10.125 * (1/8) * 0.5 = 0.6328. Total = 10.7578. The closest standard option is 10.75 m.
144
A sum of money doubles itself in 8 years at simple interest. In how many years will it triple itself?
Answer:
16 years
If it doubles in 8 years, SI = P. Rate R = (P × 100) / (P × 8) = 12.5%. To triple, SI = 2P. Time T = (2P × 100) / (P × 12.5) = 200 / 12.5 = 16 years.
145
Find the difference between simple interest and compound interest on Rs. 2000 at 5% per annum for 3 years.
Answer:
Rs. 15.25
D = P(R/100)²(3 + R/100) = 2000(5/100)²(3.05) = 2000(1/400)(3.05) = 5 × 3.05 = Rs. 15.25.
146
If the compound interest on a sum of money for 2 years at 5% per annum is Rs. 328, find the simple interest on the same sum at the same rate and for the same time.
Answer:
Rs. 320
Effective CI rate for 2 years at 5% = 10.25%. 10.25% of P = 328 => P = 3200. SI for 2 years at 5% = 10% of P. SI = 10% of 3200 = Rs. 320.
147
A sum of money amounts to Rs. 850 in 3 years and Rs. 925 in 4 years at simple interest. What is the rate of interest?
Answer:
12%
SI for 1 year = 925 - 850 = Rs. 75. SI for 3 years = 75 × 3 = 225. Principal = 850 - 225 = Rs. 625. Rate = (75 × 100) / (625 × 1) = 7500 / 625 = 12%.
148
What is the simple interest on Rs. 4000 for 6 months at 10% per annum?
Answer:
Rs. 200
Time T = 6 months = 1/2 year. SI = (P × R × T) / 100 = (4000 × 10 × 0.5) / 100 = 20000 / 100 = Rs. 200.
149
A loan was repaid in two annual installments of Rs. 121 each. If the rate of compound interest is 10% per annum, find the total sum borrowed.
Answer:
Rs. 210
Present Value of installments P = x/(1+R/100) + x/(1+R/100)². Here, x = 121, R = 10. P = 121/1.1 + 121/(1.1)² = 110 + 121/1.21 = 110 + 100 = Rs. 210.
150
A sum of Rs. 2500 is lent out in two parts, one at 5% and the other at 7% simple interest. If the total annual interest is Rs. 155, the money lent at 5% is:
Answer:
Rs. 1000
Let the sum lent at 5% be x, and at 7% be (2500 - x). SI = (x × 5 × 1)/100 + ((2500 - x) × 7 × 1)/100 = 155. 0.05x + 175 - 0.07x = 155 => 0.02x = 20 => x = 1000. The sum is Rs. 1000.