Question

a sum of money amount to Rs 840 after one year and to Rs 882 after 2 years find the rate at which interest is paid​

Answer 1

Explanation:

42/840 ×100

1/20 ×100

5%

Answer 2

Question :-

A sum of money amount to Rs 840 after one year and to Rs 882 after 2 years .find the rate at which interest is paid..?

Answer:-

Interest is paid at the rate of 5.26 %.

To find :-

Find the rate at which interest is paid ?

Step - by - step explanation :-

Let ,the principal amount be "x" and rate of interest is " r% ",

We know that,

$\small \: \bf{simple \: interest \:(SI) = \frac{Prt}{100} }$

• Amount = SI + P

$\small \: \bf{Amount \: after \: 1 \: year \: = x + \frac{x \times r \: \times 1}{100} } \\ \\ \implies \: \bf{840 = x + \frac{xr}{100} } \\ \\ \implies \bf{ 84000 = 100x + xr \: ....(1)}$

_________________________________________

Amount after 2 years,

$\implies \: \small \bf{ 882 = x + \frac{x \times r \times 2}{100} } \\ \\ \implies \small \: \bf{ \: 882 = x +\frac{2xr}{100} } \\ \\ \implies \small \bf{ 88200 = 100x + 2xr} \: ......(2)$

On solving eq.(1) and eq.(2)

Subtract eq.(1) from (2)

$\implies \: \small \: \bf{88200 - 84000 = 2xr - xr} \\ \\ \implies \: \boxed{\bf{4200 = xr}} \\ \\ \bf{ put \: the \: value \: of \: xr \: in \: eq.(1)}$

$\implies \: \bf{84000 = 100x + 4200} \\ \\ \implies \: \bf{ 100x = 79800 }\\ \\ \implies \: \boxed{\bf{x \: = 798}}$

Hence,

Principal amount = ₹ 798

_________________________________________

$\because \: \bf{ \: xr \: = 4200} \\ \\ \bf{ put \: \: x \: = 798} \\ \\ \implies \: \bf{ 798 \times r \: = 4200 } \\ \\ \implies \bf{ \: r \: = \frac{4200}{798} } \\ \\ \implies \: \boxed{ \bf{ r \: = 5.26 \: \%}}$

This is the required solution.