Questions & Answers

Question

Answers

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{\text{A}}{\text{. 10% p}}{\text{.a}}{\text{.}} \\

{\text{B}}{\text{. 8% p}}{\text{.a}}{\text{.}} \\

{\text{C}}{\text{. 7}}{\text{.5% p}}{\text{.a}}{\text{.}} \\

{\text{D}}{\text{. 6% p}}{\text{.a}}{\text{.}} \\

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Answer
Verified

Then, the amount with the simple interest for the principal amount$(P)$ in the time period of 3 years will be given as:

$\dfrac{{{\text{Prt}}}}{{{\text{100}}}}{\text{ + P = 9440 - - - - - - (i)}}$

Now the rate of interest has been increased by 25% of the initial amount, we get:

$

r' = r + 25\% {\text{of }}r \\

= 1.25r \\

$

The amount with the simple interest for the principal amount$(P)$ in the time period of 3 years will be given as:

$\dfrac{{{\text{Pr't}}}}{{{\text{100}}}}{\text{ + P = 9800 - - - - - (ii)}}$

Dividing equation (i) and equation (ii) to determine the value of the original rate of interest as:

$

\dfrac{{\left( {\dfrac{{{\text{Prt}}}}{{{\text{100}}}}{\text{ + P}}} \right)}}{{\left( {\dfrac{{{\text{Pr't}}}}{{{\text{100}}}}{\text{ + P}}} \right)}}{\text{ = }}\dfrac{{{\text{9440}}}}{{{\text{9800}}}} \\

\dfrac{{3r + 100}}{{3(1.25r) + 100}} = \dfrac{{944}}{{980}} \\

980(3r + 100) = 944(3.75r + 100) \\

2940r - 3540r = 94400 - 98000 \\

- 600r = - 3600 \\

r = \dfrac{{ - 3600}}{{ - 600}} \\

= 6\% {\text{ p}}{\text{.a}}{\text{.}} \\

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Hence, the value of the original rate of interest is 6% per annum.

Option D is correct.