At what rate per cent of simple interest does a sum of money double itself in 12?

Solution

The correct option is A12.5%Explanation for the correct option:Consider that sum is invested under simple interest.The formula for the simple interest SI is given as SI=P×R×N100 (adsbygoogle = window.adsbygoogle || []).push({}); Where , P is the principal amount, R is the percentage rate of interest per annum,N is the number of years for which the sum is invested.The amountA is given as A=P+SIAccording to given condition it is known that the amount is doubled.⇒A=2P⇒2P=P+SI⇒SI=PSubstituting the values in the formula of simple interest we get (adsbygoogle = window.adsbygoogle || []).push({}); ⇒P=P×R×8100⇒R=1008⇒R=12.5%Thus the given amount will double in 8 years at 12.5%per annum.Hence, option(A) i.e. 12.5% is the correct answer.

Solution

The correct option is A 20 yearsLet the principal be P. As per the question, Amount = 2(Principal) = 2P SI = Amount - Principal = 2P - P = P By formula, R=SI×100P×T R=P×100P×10 =10 % So, the rate is 10% per annum. Now, the sum gets tripled. A = 3(Principal) = 3P SI = 3P - P = 2P T=SI×100P×R T=2P×100P×10 = 20 years (adsbygoogle = window.adsbygoogle || []).push({});

Answer

Verified

Hint: The formula for simple interest for a principal amount P, at the rate of R % for N years is given as \[SI = \dfrac{{PNR}}{{100}}\]. Use this to equate with the given information and find the required time.Complete step-by-step answer:
The simple interest is determined by multiplying the annual interest rate by the principal amount by the number of years. If the principal amount is P, the rate is R % annually and the number of years is N, then the formula is given as follows:
\[SI = \dfrac{{PNR}}{{100}}............(1)\]
In this problem, it is given that the rate is 12 % per annum and we need to find the time in which the principal amount doubles.
Let the principal amount be P and the number of years in which the principal amount doubles be N, then the simple interest is given by the formula (1) as follows:
\[SI = \dfrac{{12PN}}{{100}}\]
Simplifying, we have:
\[SI = \dfrac{3}{{25}}PN............(2)\]
The total amount at the end of N years is the sum of simple interest and the principal amount.
\[A = P + SI\]
It is given that this amount is two times the principal amount, hence, we have:
\[2P = P + SI\]
Solving for the simple interest, we have:
\[SI = 2P - P\]
\[SI = P...........(3)\]
Equating equation (2) and equation (3), we have:
\[P = \dfrac{3}{{25}}PN\]
Canceling P on both sides, we have:
\[1 = \dfrac{3}{{25}}N\]
Solving for N, we have:
\[N = \dfrac{{25}}{3}years\]
$N$ = $8years$ $4months$
Hence, the required time is 8 years and 4 months.

Note: You might make a mistake by substituting the simple interest as equal to twice the principal amount. The amount, which is the sum of principal and simple interest is equal to twice the principal. Hence, the simple interest for the period will be equal to the principal amount.

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