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
171
The difference between simple interest and compound interest on Rs. 1200 for one year at 10% per annum reckoned half-yearly is:
Answer:
Rs. 3.00
SI for 1 year at 10% = 120. For CI reckoned half-yearly, Rate = 5%, Time = 2 cycles. Effective CI rate = 5 + 5 + 25/100 = 10.25%. CI = 10.25% of 1200 = 123. Difference = 123 - 120 = Rs. 3.00. Alternatively, D = P(R/100)² = 1200(5/100)² = 1200 × 1/400 = Rs. 3.
172
A sum of Rs. 10,000 is borrowed at 8% per annum compounded annually. If the amount is to be paid in two equal annual installments, find the approximate value of each installment.
Answer:
Rs. 5608
Let the installment be x. The present value of installments equals the principal. x/(1+R/100) + x/(1+R/100)² = P. Here R=8%, P=10000. x/(27/25) + x/(729/625) = 10000. 25x/27 + 625x/729 = 10000. (675x + 625x) / 729 = 10000. 1300x = 7290000 => x = 5607.69. Approximately Rs. 5608.
173
Find the present worth of Rs. 9261 due 3 years hence at 5% per annum compounded annually.
Answer:
Rs. 8000
Present Worth (Principal) = A / (1 + R/100)^T = 9261 / (1 + 5/100)³ = 9261 / (21/20)³ = 9261 / (9261 / 8000) = 8000. So, the present worth is Rs. 8000.
174
A sum of money placed at compound interest doubles itself in 5 years. It will amount to eight times itself at the same rate of interest in:
Answer:
15 years
The sum doubles (2 times) in 5 years. To become 8 times, we write 8 as 2³. The time required will be 3 × 5 years = 15 years.
175
What is the difference between the compound interests on Rs. 5000 for 1.5 years at 4% per annum compounded yearly and half-yearly?
Answer:
Rs. 2.04
Compounded yearly: Interest for 1st year = 4% of 5000 = 200. Amount = 5200. Interest for next half year = 2% of 5200 = 104. Total CI = 304. Compounded half-yearly: Rate = 2%, Time = 3 half-years. Amount = 5000(1.02)³ = 5000 × 1.061208 = 5306.04. Total CI = 306.04. Difference = 306.04 - 304 = Rs. 2.04.
176
If the compound interest on a certain sum for 2 years at 3% per annum is Rs. 101.50, then the simple interest on the same sum at the same rate and for the same time will be:
Answer:
Rs. 100.00
Effective CI rate for 2 years at 3% is 3 + 3 + (3×3)/100 = 6.09%. Effective SI rate is 6%. Principal = 101.50 / 0.0609 = 1666.66... SI = 1666.66 × 0.06 = Rs. 100. Alternatively, CI - SI = P(R/100)², and SI = 2PR/100. CI = SI(1 + R/200) => 101.50 = SI(1 + 3/200) = SI(203/200). SI = (101.50 × 200) / 203 = Rs. 100.
177
At what rate percent per annum will Rs. 2304 amount to Rs. 2500 in 2 years at compound interest?
Answer:
4 1/6 %
Formula: A = P(1+R/100)^T. 2500 = 2304(1+R/100)². (1+R/100)² = 2500 / 2304. Taking the square root gives 1 + R/100 = 50 / 48 = 25 / 24. R/100 = 1/24, so R = 100/24 = 25/6 = 4 1/6 %.
178
The compound interest on a sum of Rs. 5000 at 8% per annum for 9 months when interest is compounded quarterly is:
Answer:
Rs. 306.04
Rate per quarter = 8% / 4 = 2%. Time = 9 months = 3 quarters. Amount = 5000(1 + 2/100)³ = 5000(1.02)³ = 5000 × 1.061208 = 5306.04. Compound Interest = 5306.04 - 5000 = Rs. 306.04.
179
A sum of money doubles itself at compound interest in 15 years. It will become eight times of itself in:
Answer:
45 years
In compound interest, if a sum becomes x times in T years, it becomes x^n times in nT years. Here, it doubles (2 times) in 15 years. To become 8 times (which is 2³), it will take 3 × 15 = 45 years.
180
A sum of money invested at compound interest amounts to Rs. 800 in 3 years and to Rs. 840 in 4 years. The rate of interest per annum is:
Answer:
5%
The amount at the end of 3 years acts as the principal for the 4th year. The interest earned in the 4th year = 840 - 800 = Rs. 40. Rate = (40 / 800) × 100 = 5%.