All Categories MCQs
Topic Notes: All Categories
General Description
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
4091
If the difference between simple interest and compound interest for 2 years on a sum of money at 5% p.a. is Rs. 15, find the sum.
Answer:
Rs. 6000
Difference D = P(R/100)². 15 = P(5/100)² = P(1/20)² = P / 400. Therefore, P = 15 × 400 = Rs. 6000.
4092
A sum of money placed at compound interest amounts to twice itself in 4 years. In how many years will it amount to four times itself?
Answer:
8 years
In CI, the amount scales exponentially. It becomes 2 times in 4 years. To become 4 times (which is 2²), the time taken is 2 × 4 years = 8 years.
4093
The simple interest on a sum of money is 4/9 of the principal. Find the rate percent and time, if both are numerically equal.
Answer:
6.66% and 6.66 years
Let R = T = x. SI = (4/9)P. Formula: SI = (P × R × T)/100. (4/9)P = P × x² / 100. x² = 400/9, so x = 20/3 = 6.66. Hence, rate is 6.66% and time is 6.66 years.
4094
A sum of money amounts to Rs. 4624 in 2 years and Rs. 4913 in 3 years at compound interest. The sum is:
Answer:
Rs. 4096
Interest for the 3rd year = 4913 - 4624 = 289. Rate = (289 / 4624) × 100 = 6.25% = 1/16. Let sum be P. P(1 + 1/16)² = 4624 => P(17/16)² = 4624 => P × 289/256 = 4624. P = 4624 × 256 / 289 = 16 × 256 = Rs. 4096.
4095
A certain sum amounts to Rs. 7350 in 2 years and to Rs. 8575 in 3 years. Find the sum and rate percent.
Answer:
Rs. 5400, 16 2/3 %
This implies compound interest since it's an 'amount' progression. Interest for 3rd year = 8575 - 7350 = 1225. Rate = (1225 / 7350) × 100 = 16 2/3 %. Principal P = 7350 / (1 + 1/6)² = 7350 / (49/36) = 7350 × 36 / 49 = 150 × 36 = Rs. 5400.
4096
On what sum does the difference between the compound interest and the simple interest for 3 years at 10% is Rs. 31?
Answer:
Rs. 1000
Formula for 3 years difference: D = P(R/100)²(3 + R/100). 31 = P(10/100)²(3 + 10/100) = P(1/100)(3.1). 31 = P × 0.031. Therefore, P = 31 / 0.031 = Rs. 1000.
4097
A sum of money lent at compound interest for 2 years at 20% per annum would fetch Rs. 482 more, if the interest was payable half-yearly than if it was payable annually. The sum is:
Answer:
Rs. 20000
Annually: Rate = 20%, Time = 2. Effective rate = 20 + 20 + 400/100 = 44%. Half-yearly: Rate = 10%, Time = 4. Effective rate = (1.10)⁴ - 1 = 46.41%. Difference = 46.41% - 44% = 2.41%. Given 2.41% of P = 482. Therefore, P = 482 / 0.0241 = Rs. 20000.
4098
Find the difference between the compound interest and the simple interest on Rs. 32000 at 10% p.a. for 4 years.
Answer:
Rs. 2051.20
SI for 4 years = 32000 × 10% × 4 = 12800. Amount under CI = 32000(1.10)⁴ = 32000 × 1.4641 = 46851.20. CI = 46851.20 - 32000 = 14851.20. Difference = CI - SI = 14851.20 - 12800 = Rs. 2051.20.
4099
If the compound interest on a sum for 2 years at 12 1/2 % p.a. is Rs. 510, the simple interest on the same sum at the same rate for the same period of time is:
Answer:
Rs. 480
Using the relation CI = SI(1 + R/200), we have 510 = SI(1 + 12.5/200) = SI(1 + 1/16) = SI(17/16). Thus, SI = (510 × 16) / 17 = 30 × 16 = Rs. 480.
4100
The compound interest on Rs. 30000 at 7% per annum is Rs. 4347. The period (in years) is:
Answer:
2 years
Amount A = P + CI = 30000 + 4347 = 34347. A = P(1+R/100)^T => 34347 = 30000(1.07)^T. 34347 / 30000 = 1.1449. Since 1.07² = 1.1449, the time period T is 2 years.