Simple interest on a certain sum of money for 4 years at 5% per annum is half the compound interest on Rs. 3000 for 2 years at 10% per annum. The sum placed on simple interest is:a)Rs.1575b)Rs. 2200c)Rs. 1200d)Rs. 1625Correct answer is option 'A'. Can you explain this answer?

Question

Answer

Answer

According to given question compound interest is 630.
Then, SI = 315
I = (PTR)/100
We get 1575

Answer

C.I = P[(1 + r/100)n - 1]
C.I = 3000[(1 + 0.10)2 - 1]
= 3000(1.21 - 1)
⇒ 3000 * 0.21
⇒ 630
S.I = 630/2
⇒ 315
As we know that, P = (SI * 100)/(R * T)
⇒ (315 * 100)/(4 * 5)
⇒ 1575

Answer

Given: Simple interest on a certain sum of money for 4 years at 5% per annum is half the compound interest on Rs. 3000 for 2 years at 10% per annum.

To Find: The sum placed on simple interest.

Solution:

Let the sum placed on simple interest be Rs. P.

According to the question,

Simple Interest (SI) = (P × 4 × 5)/100

Compound Interest (CI) = P [1 + (10/100)]² - P

Given that SI = (1/2) CI

=> (P × 4 × 5)/100 = (1/2) [P [1 + (10/100)]² - P]

=> 20P = P [1 + (10/100)]² - P

=> 20 = [1 + (10/100)]² - 1

=> 21 = [1 + (10/100)]²

=> 1 + (10/100) = √21

=> P = (CI + P)/2

=> P = (3000 [1 + (10/100)]²)/2

=> P = (3000 × 11 × 11)/200

=> P = 1815

Therefore, the sum placed on simple interest is Rs. 1575. (Option A)

Hence, option A is the correct answer.

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