Question

A certain amount becomes Rs 5760 in 2 years and Rs 6912 in 3 years. what is the principal, amount and the rate of interest?

Answer 1

the principal Rs. 3456 and rate of interest is 100/3 %.

A certain amount becomes Rs. 5760 in 2 years and Rs. 6912 in 3 years.

We have to find the principal amount and rate of interest.

Here, question is not providing the details of interest. so we should understand, it is the question of Simple interest.

Let principal is P and rate of interest is r.

case 1 : A = 5760 , t = 2 years

⇒SI = (P × r × t)/100

= (P × r × 2)/100

= 2Pr/100

now, A = P + SI

⇒5760 = P + 2Pr/100 = P(100 + 2r)/100 ...(1)

case 2 : A = 6912 , t = 3 years

⇒SI = (P × r × t)/100

= (P × r × 3)/100

= 3Pr/100

now, A = P + SI

⇒6912 = P + 3Pr/100 = P(100 + 3r)/100 ...(2)

Dividing equations (1) by (2), we get

⇒5760/6912 = {P(100 + 2r)/100}/{P(100 + 3r)/100}

⇒5/6 = (100 + 2r)/(100 + 3r)

⇒500 + 15r = 600 + 12r

⇒3r = 100

⇒r = 100/3 = 33.33 %

Now from equations (1),

5760 = P + 2P × (100/3)/100

⇒5760 = P + 2P × 1/3 = 5P/3

⇒P = 3456

Therefore the principal Rs. 3456 and rate of interest is 100/3 %.

Answer 2

$\huge\red{A}\pink{N}\orange{S} \green{W}\blue{E}\gray{R} =$

Let the amount (principal) be = X

Assuming Simple Interest:-

X + 2XY = 5760

X + 3XY = 6912

Multiplying top by 3 and bottom by 2 we get

3X + 6XY - 5760 X 3

2X + 6 XY = 6912 X 2

Subtracting we get

3X - 2 X + 6XY-6XY = 5760 x 3 - 6912 x 2

X = 17280 - 13824 = 3456.00

So amount is Rs. 3456.00

Now 3456 + 2 X 3456 X Y = 5760

6912 Y = 5760 - 3456 = 2304

Y = 2304/6912 - 1/3

So Rate of interest is a whopping 1 /3 or 33.33%