Question

a sum of 2100 is lent out in two parts if the interest on one part at 9% p.a. for 5 years is equal to interest on the other part at 6/1/4 % p.a. for years , find the part lent out at 9% p.a.​

Answer 1

Answer:

750

Step-by-step explanation:

Let x rupees be put at 9% p.a. for 5 years,than interest

\begin{gathered} \frac{x \times 9 \times 5}{100} \\ \\ = \frac{9x}{20} \\ \\ \end{gathered}

100

x×9×5

=

20

9x

Amount left with (2100-x) Rs be put at 25/4% p.a. for 4 years

\begin{gathered} \frac{(2100 - x) \times 25 \times 4}{4 \times 100} \\ \\ = \frac{(2100 - x)}{4} \\ \\ \end{gathered}

4×100

(2100−x)×25×4

=

4

(2100−x)

Since both the interest are equal,so equate these two interest calculated above

\begin{gathered} \frac{9x}{20} = \frac{2100 - x}{4} \\ \\ \frac{9x}{5} = 2100 - x \\ \\ 9x = 5(2100 - x) \\ \\ 9x =10500 - 5x \\ \\ 9x + 5x = 10500 \\ \\ 14x = 10500 \\ \\ x = \frac{10500}{14} \\ \\ x = 750 \\ \\ \end{gathered}

20

9x

=

4

2100−x

5

9x

=2100−x

9x=5(2100−x)

9x=10500−5x

9x+5x=10500

14x=10500

x=

14

10500

x=750

So the money lend at 9% p.a is 750/- Rs.

Hope it helps you.