The amount obtained by investing a certain sum at r% p. a. for 4 years

1.	The amount obtained by investing a certain sum at r% p. a. for 4 years simple interest is equal to the simple interest on the same sum at the same rate for 14 years. What is the value of r?1. 102. 83. 94. 12
Answer» Correct Answer - Option 1 : 10 Given: Amount obtained at a sum for 4 years at r % = SI on the same sum at r % for 14 years Formula used ; Amount = Principal + SI \(SI = {P\times r\times t \over 100}\) Calculation : Let the principal be P According to the question The amount for 4 years at r % = SI for 14 years at r % P + SI for 4 years at r % = SI for 14 years at r % ⇒ P + \({P\times r\times t \over 100}\) = \({P\times r\times T \over 100}\) P + \({P\times r\times 4 \over 100}\) = \({P\times r\times 14 \over 100}\) ⇒ P = (14Pr/100) - (4Pr/100) ⇒ P = Pr/10 ⇒ r = 10 ∴ The value of 'r' is 10 %

The amount obtained by investing a certain sum at r% p. a. for 4 years simple interest is equal to the simple interest on the same sum at the same rate for 14 years. What is the value of r?1. 102. 83. 94. 12

Answer» Correct Answer - Option 1 : 10

Given:

Amount obtained at a sum for 4 years at r % = SI on the same sum at r % for 14 years

Formula used ;

Amount = Principal + SI

\(SI = {P\times r\times t \over 100}\)

Calculation :

Let the principal be P

According to the question

The amount for 4 years at r % = SI for 14 years at r %

P + SI for 4 years at r % = SI for 14 years at r %

⇒ P + \({P\times r\times t \over 100}\) = \({P\times r\times T \over 100}\)

P + \({P\times r\times 4 \over 100}\) = \({P\times r\times 14 \over 100}\)

⇒ P = (14Pr/100) - (4Pr/100)

⇒ P = Pr/10

⇒ r = 10

∴ The value of 'r' is 10 %

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