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. 10
2. 8
3. 9
4. 12
1. 10
2. 8
3. 9
4. 12
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 %