The ratio of 3 years of C.I. and S.I. of one year on a certain sum of

1.	The ratio of 3 years of C.I. and S.I. of one year on a certain sum of money is 4.75 ∶ 1. Find rate percent?1. 50%2. 40%3. 48%4. 20%
Answer» Correct Answer - Option 1 : 50% Given: The ratio of 3 years of C.I. and S.I. of one year on a certain sum of money is 4.75 ∶ 1. Formula used: (x + y)³ = x³ + y³ + 3xy(x + y) S.I. = (P × R × T)/100 A = P(1 + R/100)n Where A → amount n → time S.I. → Simple Interest P → Principal R → Rate T → Time Calculations: Let the sum of money be Rs. P. and rate of interest be R% p.a. Compound interest for 3 years = P[(1 + R/100)³ - 1] ⇒ P[1 + 3 × 1 × (R/100)(1 + R/100) + (R/100)³ -1] ⇒ P(R/100)(3 + 3 × R/100 + R²/10000) Simple interest for one year = (P × R × 1)/100 According to the question, ⇒ {P(R/100)(3 + 3 × R/100 + R2/10000)}/(P × R × 1)/100 = 4.75/1. ⇒ 3 + 3 × (R/100) + R²/10000 = 4.75 ⇒ R2/10000 + 3 × (R/100) - 1.75 = 0 ⇒ R² + 300R - 17500 = 0 ⇒ R2 + 350R - 50R - 17500 = 0 ⇒ R(R + 350) - 50(R + 350) = 0 ⇒ (R + 350)(R - 50) = 0 Thus R = - 350% (not valid) , or R = 50% ∴ The rate is 50%.

The ratio of 3 years of C.I. and S.I. of one year on a certain sum of money is 4.75 ∶ 1. Find rate percent?1. 50%2. 40%3. 48%4. 20%

Answer» Correct Answer - Option 1 : 50%

Given:

The ratio of 3 years of C.I. and S.I. of one year on a certain sum of money is 4.75 ∶ 1.

Formula used:

(x + y)³ = x³ + y³ + 3xy(x + y)

S.I. = (P × R × T)/100

A = P(1 + R/100)n

Where A → amount

n → time

S.I. → Simple Interest

P → Principal

R → Rate

T → Time

Calculations:

Let the sum of money be Rs. P. and rate of interest be R% p.a.

Compound interest for 3 years = P[(1 + R/100)³ - 1]

⇒ P[1 + 3 × 1 × (R/100)(1 + R/100) + (R/100)³ -1]

⇒ P(R/100)(3 + 3 × R/100 + R²/10000)

Simple interest for one year = (P × R × 1)/100

According to the question,

⇒ {P(R/100)(3 + 3 × R/100 + R2/10000)}/(P × R × 1)/100 = 4.75/1.

⇒ 3 + 3 × (R/100) + R²/10000 = 4.75

⇒ R2/10000 + 3 × (R/100) - 1.75 = 0

⇒ R² + 300R - 17500 = 0

⇒ R2 + 350R - 50R - 17500 = 0

⇒ R(R + 350) - 50(R + 350) = 0

⇒ (R + 350)(R - 50) = 0

Thus R = - 350% (not valid) , or R = 50%

∴ The rate is 50%.