Question

Divide Rs. 1080 into two parts such that if the first be lent at
6% for 5 years and second be lent at 10% for 4 years
, the
interest may be in the ratio 3 : 5.​

Answer 1

Given:

Divide Rs. 1080 into two parts such that if the first be lent at 6% for 5 years and the second be lent at 10% for 4 years, the interest may be in the ratio 3 : 5.​

To find:

The two parts

Solution:

We know,

$\boxed{\bold{Simple \:Interest = \frac{P \times R \times T}{100} }}$

For the first part interest:

The rate of interest, R = 6%

The no. of years, T = 5 years

Let "x" be the sum of money lent.

∴ $Simple \:Interest = \frac{x \times 6 \times 5}{100} = \frac{30x}{100}$

For the second part interest:

The rate of interest, R = 10%

The no. of years, T = 4 years

Let "(1080 - x)" be the sum of money lent.

∴ $Simple \:Interest = \frac{(1080 - x) \times 10 \times 4}{100} = \frac{40(1080 - x)}{100}$

Now, as given in the question, we can form the equation as:

$\frac{First\:part}{Second\:part} = \frac{3}{5}$

$\implies \frac{ \frac{30x}{100}}{ \frac{40(1080 - x)}{100}} = \frac{3}{5}$

$\implies \frac{ 30x}{ 40(1080 - x)} = \frac{3}{5}$

$\implies 150x = 120(1080 - x)$

$\implies 150x = 129600 - 120x$

$\implies 270x = 129600$

$\implies \bold{x = 480}$

∴ $\bold{1080 - x} = 1080 - 480 = \bold{600}$

Thus,

$\boxed{\bold{1st \:part \:\rightarrow \underline{Rs.\: 480}}}\\\\\boxed{\bold{2nd \:part \:\rightarrow \underline{Rs.\: 600}}}$

--------------------------------------------------------------------------------------

Also View:

divide rupees 3000 into 2 parts such that the simple interest on the first part for 4 years at 8% per annum is = to the simple interest on the 2 part for 2 years at 9% per annum?

brainly.in/question/2672317

divide RS. 6000 into 2 parts so that the simple interest on the first part for 9 months at 12% per annum is equal to the simple interest on the second part for 1.5 years at 10% per annum. ​

brainly.in/question/9893973

Divide Rs.8000 into two parts such that if one part be lent at 15/2℅ p.a. for 2years and the other at 8℅ p.a. for three years the total interest received is Rs.1416

brainly.in/question/6287664

Divide Rs. 6000 into two parts so that simple interest on the first part for 2 years at 6% p.a. may be equal to the simple interest on the second part for 3 years at 8% p.a.

brainly.in/question/6837916