Question

यदि कोई धन 3 साल में
अपने आप का 8 गुना हो
जाता है, तो वहीं धन
अपने आप का 128 गुना
कितने वर्षों में हो जायेगा।


Pls answer​

Answer 1

Answer:

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Answer 2

Given:

यदि कोई धन 3 साल में अपने आप का 8 गुना हो जाता है, तो वहीं धन अपने आप का 128 गुना कितने वर्षों में हो जायेगा।

To find:

तो वहीं धन अपने आप का 128 गुना कितने वर्षों में हो जायेगा।

Solution:

We know,

$\boxed{\bold{A = P [1 + \frac{R}{100}]^n }}$

where A = amount, P = principal, R = rate of interest and n = no. of years  

Let "P" represents the sum of money.

When the amount becomes 8 times of the principal:

A = 8P

n = 3 years

By using the above formula, we get

$8P = P [1 + \frac{R}{100} ]^3$

$\implies 8 = [1 + \frac{R}{100} ]^3$

$\implies 2^3 = [1 + \frac{R}{100} ]^3$

taking cube root on both the sides

$\implies 2 = 1 + \frac{R}{100}$

$\implies 1 = \frac{R}{100}$

$\implies \bold{R = 100\%}$

When the amount becomes 128 times of the principal:

A = 128P

Let "n" represents the no. of years the amount would take to become 128 times the principal.

By using the above formula, we get

$128P = P [1 + \frac{100}{100} ]^n$

$\implies 128 = [1 + 1 ]^n$

$\implies 128 = [2 ]^n$

$\implies 2^7 = 2^n$ . . . [∵ 128 = 2⁷]

$\implies \bold{n = 7\:years}$

Thus, the sum of money becomes 128 times in → 7 years.

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