Question

A certain sum amounts to ₹5916 in 3 years and to ₹6960 in 5 years at simple interest.Find the sum and the rate per cent per annum.
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Answer 1

Answer:

.

Explanation:

Formula to find The final amount after a principal amount p is invested at rate of interest r ( in decimal ) in time

A = p ( l+RT)

i.e 5916 = p ....1 by give

6960 = p (1+5r)....2 by given

Divided Equation 2 by 1

6960/5916 = p ( 1 +5r)/p ( 1+3r)

20/17 = (1 +5r)/( 1+3r)

20 ( 1+3r) = 17 ( 1+5r)

20 + 60 r = 17 + 85 r

85 - 60 = 17 -20

25 r = 3

r = 3/25

Put Value r in (1)

5916 = p ( 1+3(25/3)

5916 = p ( 26)

p = 5916/26

p = 227.54

The value r in percent = 3/25×100

4×3 = 12%

So your answers is 12%

thanks dear friend

Answer 2

$\huge\color{lime}{Añswër° ᭄}$

$\bold\blue{★Solution:-}$

‎ ‎ ‎ ‎ ‎ ‎‎ ‎ ‎ ‎ ‎ ‎ ‎‎★We know:-

S.I. for 2 years = (Amount after 5 years) - (Amount after 3 years)

‎ ‎ ‎ ‎ ‎ ‎ ‎‎ ‎ ‎ ‎ ‎ ‎ ‎‎ ‎ ‎ ‎ ‎ ‎ ‎= ₹ (6960 - 5916) = ₹ 1044.

S.I. for 1 year =

$\green₹ (\frac{1044}{2} ) = ₹ \: 522$

S.I. for 3 years = ₹ (522 × 3) = ₹ 1566

‎ ‎ ‎ ‎ ‎ ‎‎⇒Sum = (Amount after 3 years) - (S.I. for 3 years)

‎‎ ‎ ‎ ‎ ‎ ‎ ‎‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎‎ ‎ ‎ ‎= ₹ (5916 - 1566) = ₹ 4350.

★Now, P = ₹ 4350, S.I. = ₹ 1566, T = 3 years.

‎ ‎ ‎ ‎ ‎ ‎‎ ‎ ‎ ‎ ‎ ‎ ‎‎$\bold\red{†Required \: formula†}$

$R = \frac{100 \times S.I.}{P \times T}$

$➜(\frac{100 \times 1566}{4350 \times 3} )\%p.a$

‎ ‎ ‎ ‎ ‎ ‎‎ ‎ ‎ ‎ ‎ ‎ ‎‎= 12% p.a

‎ ‎ ‎ ‎ ‎ ‎‎$\bold\pink{★Note:-}$

Hence , the required sum is ₹ 4350 and the rate of interest is 12% p.a.

$\bold\green{★hope \: it \: will \: help \: u..} \\▬▬▬▬▬▬▬▬★▬▬▬▬▬▬▬▬▬$