Question

A sum of money invested at 6% p.a. simple interest for a certain period of time yields $960 as interest. If this sum had been invested for 5 years more, it would have yielded $2160 as interest. Find the sum.
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Answer 1

Step-by-step explanation:

According to the problem,

Let sum be P

R=6%

Time=Tyears

S.I=

100

P×6×T

S.I=Rs960

100

P×6×T

=960

P×T=16000----------------(1)

Now For sum

Sum=RsP,R=6%,T=5years

S.I=

100

P×6×(T+5)

=2160

100

P×6×T

+

100

P×6×5

=2160

100

16000×6

+

100

P×30

=2160

100

P×30

=2160−960

100

P×30

=1200

P=

30

1200×100

=Rs.4000

Therefore the Sum is Rs, 4000.

Answer 2

➸ Given:-

• Rate of Interest = 6%
• Simple Intrest = $960
• Time = 5 years
• Simple Intrest = $2160

☣ To Find:-

• The Sum.

☢ Solution:-

Let, The Sum be P

Rate = 6%

Time = T years

$\pink{\sf{あ\; Simple\; Intrest = \frac{PTR}{100}}}$

Where P is Principal, R is Rate of Intrest & T is Time Taken.

Simple Intrest = $960

$\frac{P \times 6 \times T}{100} = 960 \\ P \times 6 \times T = 960 \times 100 \\ P \times T = \frac{960 \times 100}{6} \\ P \times T = 160 \times 100 \\ P \times T = 16000$

☞ P×T = $16000

Now For The Required Sum

Sum = P

Rate = 6%

Time = 5 years → Total Time = (T+5) years

$\frac{P \times 6 \times (T + 5)}{100} = 2160 \\ (\frac{P \times 6 \times T}{100}) + ( \frac{P \times 6 \times 5}{100} ) = 2160 \\ (\frac{16000 \times 6}{100} ) + ( \frac{P \times 30}{100} ) = 2160 \\ (160 \times 6 )( \frac{P \times 30}{100} ) = 2160 \\ \frac{p \times 30}{100} = 2160 - 960 \\ P \times 30 = 1200 \times 100 \\ P = \frac{1200 \times 100}{30} \\ P = 40 \times 100 \\ P = 4000$

Required Sum

• $\Large\red{\bold{\ 4000}}$

$\boxed{\tt{@MrMonarque}}$

Hope It Helps You ✌️