Question

a certain sum of money amounts to rs704 in 2 years and rs800 in 5years. find the principle and rate of interest​

Answer 1

Answer:

p= 640

r = 5%

Step-by-step explanation:

a1 = 704

t1 = 2

a2 = 800

t2 = 5

If it's simple interest,

a = p(1 + rt)

704 = p(1 + 2r)

Eqn.1=> p + 2pr = 704

800 = p(1 + 5r)

Eqn. 2=> p + 5pr = 800

Solving both equations simultaneously,

Multiplying eqn. 1 by 5 and eqn.2 by 2.

Subtracting Eqn. 2 from eqn. 1,

5p + 10pr = 3520

-2p - 10pr = -1600

3p = 1920

p = 640

Putting the value of p in equ.2,

3200r = 160

r = 0.05 = 5%

Answer 2

principle is rs640 and rate of interest is 5%

Step-by-step explanation:

given :

  Amount a1 = 704 , time t1 = 2years

 Amount a2 = 800 , time t2 = 5years

Amount  =  P(1+rt)

$704 = P(1+2r)$ ----> equa 1

$800 = P(1+5r)$ -----> equa 2

multiply equa 1 by 5 and multiply equa 2 by 2

$3520 = 5P + 10 pr\\1600 = 2P + 10 pr$

subtract both equations we get,

$1920 = 3P\\P = 640$

substitute the value of P and  find r

$704 = 640 + 1280r\\64 = 1280r\\r = 64 / 1280\\r = 1 / 20\\r = 0.05\\r = 5%$

Therefore, principle is rs 640 and rate of interest is 5%