Question

15. A sum of money lent at S.I amounts to 8944 in 4 years and 11,752 in 7 years.
Find the sum of money and the rate of interest.​

Answer 1

sum of money is 5200 and rate of interest is 18% per annum

let sum of money is P and rates of interest is r % per annum.

case 1 : A = 8944 , t = 4yrs

using formula, A = P + P × r × t/100

8944 = P + Pr4/100 = P + Pr/25 = P(1 + r/25).....(1)

case 2 : A = 11752 , t = 7yrs

11752 = (P + P × r × 7/100) = P(1 + 7r/100) .....(2)

from equations (1) and (2) we get,

8944/11752 = (1 + r/25)/(1 + 7r/100)

⇒86/113 = (25 + r)4/(100 + 7r)

⇒8600 + 86 × 7r = 113(100 + 4r)

⇒8600 + 602r = 11300 + 452r

⇒(602 - 452)r = 11300 - 8600 = 2700

⇒150r = 2700

⇒r = 18

hence, rate of interest is 18% per annum.

and P = 8944/(1 + 18/25) = 8944 × 25/43

= 298 × 25 = 5200

also read similar questions : A sum of money lent out at simple interest amounts to ₹ 2200 in one year and ₹ 2800 in 4 years. Find the sum of money an...

https://brainly.in/question/1196663

A sum of money lent out at simple interest amounts to 2200 rupees in one year and to 2800 rupees in four years. Find the...

https://brainly.in/question/36660

Answer 2

$\bf{\underline{\underline{Answer:}}}$

$\therefore\bf {5200} \:rupees$

$\bold{\underline {Given:}}$

• A sum of money lent at S.I amounts to 8944 in 4 years

• and 11,752 in 7 years

$\bold{\underline {To\:find:}}$

• the sum of money and the rate of interest =?

$\bf{\underline{\underline{Step\: by\: step \:explanation:}}}$

Let sum of money is P and rates of interest is r % per annum.

${\bf{\red{Method : 1}}}$

• Amount = ₹ 8944

• Time = 4 years

By,

$\boxed{\sf{A = P + P × r × \dfrac{t} {100}}}$

$8944 = P +\dfrac{Pr4} {100} =P +\dfrac{Pr} {25} = P\left(1 +\dfrac{r}{25}\right)$ .....(1)

${\bf{\red{Method : 2}}}$

• Amount = ₹ 11752

• Time = 7 years

$11752 =\left (P + P × r ×\dfrac{7} {100} \right) = P\left(1 + \dfrac{7r} {100} \right)$ .....(2)

from equations (1) and (2) we get,

$\dfrac{8944}{11752} = \dfrac{\left(1 + \dfrac{r} {25} \right)}{\left(1 + \dfrac{7r} {100}\right)}$

$\implies\dfrac{86}{113} = (25 + r)\dfrac{4}{(100 + 7r)} \\ \\</p><p></p><p>\implies 8600 + 86 × 7r = 113(100 + 4r)\\ \\</p><p></p><p>\implies 8600 + 602r = 11300 + 452r\\ \\</p><p></p><p>\implies(602 - 452)r = 11300 - 8600 = 2700\\ \\</p><p></p><p>\implies 150r = 2700\\ \\</p><p></p><p>\implies r = 18$

Hence, rate of interest is 18% per annum.

And,

$P = \dfrac{8944} {\left(1 + \dfrac{18} {25}\right)} = \cancel{8944} ^{298}× \dfrac{25} {\cancel{43}}$

= 298 × 25 = 5200