Question

After how many years a sum of rupees will be two times at the rate of interest
6 Whole1/4% per annum ?​

Answer 1

Given :-

$rate\% = 6 \dfrac{1}{4} = \dfrac{25}{4}$

• Principal becomes double in a particular period of time

To find :-

Time

FORMULA TO USE :-

$simple \: interest = \dfrac{principal \times time \times rate}{100}$

Let us assume principal to be ₹x and time to be y.

Amount = 2 times principal = ₹2x

Hence, interest = 2x - x = ₹x

By substituting the values

$x = \dfrac{x \times y \times 25 }{100 \times 4}$

$x = \dfrac{xy \times \cancel{25}}{ \cancel{100} \times 4}$

$x = \dfrac{xy}{4 \times 4}$

$x = \dfrac{xy}{16}$

By transposing 16 to the LHS (Left Hand Side),

$16(x) = xy$

$16x = xy$

Transposing x to the LHS (Left Hand Side),

$\dfrac{16x}{x} = y$

$\dfrac{16 \not x}{ \not x} = y$

$16 = y$

Therefore, in 16 years the principal will become double.

Some more formulas :-

$\dfrac{simple \: interest \times 100}{time \times rate} = principal$

$\dfrac{simple \: interest \times 100}{principal \times time} = rate$

$\dfrac{simple \: interest \times 100}{principal \times rate} = time$