Divide Rs 2,760 in to two parts such that when these are invested for 2 and 4 years, respectively, at the rate of 5%

Divide Rs 2,760 in to two parts such that when these are invested for 2 and 4 years, respectively, at the rate of 5% per annum simple interest, the amounts received are equal. What is the second part (in Rs) invested?

Options
a) 1100
b) 1500
c) 1320
d) 1440

Solution

As per question
Let First Part is a and second part is b
$a +\frac {( a \times r \times t)}{100}$ = $b +\frac {( b \times r \times t)}{100}$
$a +\frac {( a \times 5 \times 2)}{100}$ = $b +\frac {( b \times 5 \times 4)}{100}$
$a +\frac { 10a}{100}$ = $b +\frac {20b}{100}$
$a +\frac { a}{10}$ = $b +\frac { b}{5}$
$\frac { 11a}{10}$ = $\frac {6b}{5}$
11a = 12b
$\frac ab = \frac {12}{11}$
a = 12
b = 11
Sum of ratio = 12 + 11 = 23
Invested second part ( b ) = $\frac {2760}{23} \times 11$ = 1320