Question

what principal will amount to 9856 in two years if rate of interest for successive years are 10% and12% respectively

Answer 1

Let the Principal was P
for first year, R = 10%
Interest = PTR/100 = P×1×10/100 = 0.1P
Amount at the end of 1st year = P + 0.1P = 1.1P

For 2nd year,
Principal = 1.1P
R = 12%
Interest = PTR/100 = 1.1P×1×12/100 = 0.132P

Amount at the end of 2nd year = 1.1P + 0.132P = 1.232P

It is given that amount is 9856

⇒1.232P = 9856

⇒ P = 9856/1.232 

⇒ P = Rs. 8000

Principal was Rs. 8000 

Answer 2

$Hey \: There \:$

$Let \: x \: be \: the \: principal.$
$P = x \: Rs.$
$rate = 10\%$
$n = 1 \: year$
$A = P \: (1 + \frac{r}{100} ) {}^{n}$
$A = x \: (1 + \frac{10}{100} ) {}^{1}$
$A = 1.1x \: Rs.$

$Now, \: \: \: P = 1.1x \: rs.$
$rate = 12\%$
$n = 1 \: year$
$A = P \: (1 + \frac{r}{100} ) {}^{n}$
$A = 1.1x \: (1 + \frac{12}{100} ) {}^{1}$
$A \: = \: 1.232x \: Rs.$

$A.T.Q.$
$1.232x = 9856$
$x = \frac{9856}{1.232}$
$x = 8000 \: Rs.$

$Therefore, \: principal \: is \: Rs. \: 8000.$