Question

A sum of money invested at 6% per annum simple interest for a certain period of time yields Rs.960as interest. If this
had been invested for 5 years more, it would have yielded Rs.2160as interest. Find the sum.​

Answer 1

Answer:-

Let the sum of money be x and original time be y

So simple Internet for y yrs time = 960

x(6%)(y) = 960

xy = 16000------------ (1)

Now simple intrest for y + 5 yrs time = 2160

x(6%)(y + 5) = 2160

x(y + 5) = 36000

xy + 5x = 36000

From eq1

16000 + 5x = 36000

5x = 20000

x = 4000rs

Put x in eq(1)

4000y = 16000

y = 4yrs

Answer 2

Answer:

• Rate of Interest = 6% per annum
• SI after certain period = Rs. 960
• SI after 5 more years = Rs. 2160
• Find Principal.

We know that Simple Interest Increase with constant rate and that's Equal Every Year.

↠ SI of 5 years = After 5 yr – Certain Period

↠ SI of 5 years = Rs. 2160 – Rs. 960

↠ SI of 5 years = Rs. 1200

↠ SI of 1 years = $\sf\frac{Rs.\:1200}{5}$

↠ SI of 1 years = Rs. 240

• So we Get that Simple Interest of 1 year is Rs. 240

$\underline{\bigstar\:\:\textsf{Time Period :}}$

$:\implies\sf Time=\dfrac{Certain \:Period \:SI}{SI \: of \:1\:year}\\\\\\:\implies\sf Time=\dfrac{Rs.\:960}{Rs.\:240}\\\\\\:\implies\sf Time = 4 \:years$

$\rule{150}{1}$

$\underline{\bigstar\:\:\textsf{According to the Question :}}$

$\frak{we\:have}\begin{cases}\textsf{Simple Interest = Rs. 960}\\\textsf{Rate = 6\% p.a.}\\\textsf{Time = 4 years}\\\textsf{Principal = ?} \end{cases}$

$\dashrightarrow\tt\:\: Simple\: Interest=\dfrac{Principal \times Rate \times Time}{100}\\\\\\\dashrightarrow\tt\:\:960 = \dfrac{Principal \times 6 \times 4}{100}\\\\\\\dashrightarrow\tt\:\:960 \times \dfrac{100}{(6 \times 4)} = Principal\\\\\\\dashrightarrow\tt\:\:40 \times 100 = Principal\\\\\\\dashrightarrow\:\:\underline{\boxed{\tt Principal = Rs. \:4000}}$

⠀

$\therefore\:\underline{\textsf{Hence, Principal will be \textbf{Rs. 4000}}}$