Question

A sum of money lent by Hari at simple interest becomes double of itself in 8 years. Then the sum will triple itself in
(a) 16 years
(b) 15 years
(c) 20 years
(d) 24 years

Answer 1

Hint: Firstly assume the principal amount to be any variable and then find the increase in the principal amount that is the simple interest SI by using the given conditions. Then find the rate of interest R using the formula \[SI=\dfrac{PRT}{100}\]. After finding the rate of interest R substitutes its value in the formula and finds the time T for the interest amount A to be triple of the principal amount and finds the final answer.

Complete step-by-step answer:
We know the formula for simple interest is given as \[SI=\dfrac{PRT}{100}\], where SI is the simple interest, P is the principal amount on which interest is being applied, R is the rate of interest per year in percentage and T is the time in years.
Let the principal amount P = k rupees
It is said that the interest amount doubles itself in 8 years. Therefore the amount A after adding simple interest SI is equal to the twice of the principal amount P and time T = 8 years.
The above equation can be expressed mathematically as,
A = 2P
Substituting the value of P in the above equation,
A = 2k
Therefore the increase in amount can be calculated as,
SI = A – P
Substituting the A = 2k and P = k in the above equation we get,
SI = 2k – k
On subtracting k from 2k the simple interest SI turns out to be,
SI = k
Applying the mentioned formula for simple interest to find the rate of interest R we get,
Substituting the values of SI, P and T in the expression,
\[k=\dfrac{k\cdot R\cdot 8}{100}\]
Multiplying 100 on both sides,
\[k\cdot 100=k\cdot R\cdot 8\]
On dividing with 8k on both sides we get,
\[\dfrac{k\cdot 100}{8k}=R\]
Dividing 8k by k and simplifying the expression we get,
\[R=\dfrac{100}{8}\]
By dividing 100 with 8 we get the rate of interest as,
R = 12.5%
For the amount A to get triple, the interest amount will be equal to thrice of principal amount keeping the rate of interest R same.
The above said statement can be expressed mathematically as,
A = 3P
By substituting the value of P in the above equation we get,
A = 3k
Therefore the increase in amount can be calculated as,
SI = A – P
Substituting the A = 3k and P = k in the above equation we get,
SI = 3k – k
On subtracting k from 3k the simple interest SI turns out to be,
SI = 2k
Applying the above mentioned formula for simple interest to find the time T for the SI amount to get triple we get,
Substituting the values of SI, P and R in the expression,
\[2k=\dfrac{k\cdot 12.5\cdot T}{100}\]
Multiplying 100 on both sides,
\[2k\cdot \left( 100 \right)=k\cdot 12.5\cdot T\]
On dividing with 12.5k on both sides we get,
\[\dfrac{2k\cdot \left( 100 \right)}{12.5k}=T\]
Dividing 100 with 12.5 and simplifying the expression we get,
T = 2(8)
By multiplying 8 with 2 we get the time T in years as,
T = 16
Therefore the time taken for the interest amount to get triple of its principal value is 16 years.
Hence option (a) is the correct answer.

Note: A possible mistake that you may encounter could be mistaking the interest amount A with simple interest SI. Simple interest SI is the increase in the principal amount after the interest is applied and interest amount A is the sum of principal amount P and simple interest SI. Alternatively this question can also be solved by using the formula \[A=P\left( 1+RT \right)\], where the variables have their general meaning as used above.