The difference between the simple interest and compound interest on a certain sum for 2 years and 5% p.a. is ₹100. What is the sum?
Answers
Answer:
Your answer
Given,
Time = 3 years
Rate = 5% p. a.
Let the sum be ₹ P.
\begin{gathered}si = \frac{p \times r \times t}{100} \\ \\ \: \: \: \: \: = \frac{p \times 5 \times 3}{100} \\ \\ \: \: \: \: \: = \frac{3p}{20} \\\end{gathered}
si=
100
p×r×t
=
100
p×5×3
=
20
3p
CI = { p × ( 1 + r / 100 )^t – p }
= { p × ( 1 + 5 / 100 )^3 – p }
= { p × ( 1 / 20 )^3 – p }
= ( p × 21/20 × 21/20 × 21/20 – p)
\begin{gathered}= \frac{9261p}{8000} - p \\ \\ = \frac{9261p - 8000p}{8000} \\ \\ = \frac{1261p}{8000}\end{gathered}
=
8000
9261p
−p
=
8000
9261p−8000p
=
8000
1261p
According to question,
CI – SI = 183
\begin{gathered}\frac{1261p}{8000} - \frac{3p}{20} = 183 \\ \\ \frac{1261p - 1200p}{8000} = 183 \\ \\ \frac{61p}{8000} = 183 \\ \\ 61p = 183 \times 8000 \\ \\ p = \frac{183 \times 8000}{61} \\ \\ p = 24000\end{gathered}
8000
1261p
−
20
3p
=183
8000
1261p−1200p
=183
8000
61p
=183
61p=183×8000
p=
61
183×8000
p=24000
Hence, the sum is ₹ 24000
Hope it help you
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