Question

9. A person invested
Rs. 10,000 at 6% p.a.Rs.8,000
at 5%p.a.
And Rs.6000 at 4%
p.a.simple interest. The
average rate of simple interest
is
(a) 5 (b) 5.17 (c) 5.57
(d) 5.27​

Answer 1

➤ Correct Question :-

A person invested ₹10000 at 6%, ₹8000 at 5% and ₹6000 at 4% at 1 year. Find the average rate of simple interest of all the three investments.

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★ How to do :-

Here, we are given that a person invests some money three times for each one year. We are asked to find the average rate of simple interest of all the three investments. So, first we should find the simple interest of all the three investments separately and then we should find the average or also it's known as mean. The formula required for each steps will be provided while solving the problem. So, let's solve!!

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➤ Solution :-

Simple Interest (1) :-

${\tt \leadsto \underline{\boxed{\tt \dfrac{P \times R \times T}{100}}}}$

Substitute the given values.

${\tt \leadsto \dfrac{10000 \times 6 \times 1}{100}}$

Cancel the zeros in numerator and denominator.

${\tt \leadsto \dfrac{100 \cancel{00} \times 6 \times 1}{1 \cancel{00}} = \dfrac{100 \times 6 \times 1}{1}}$

Multiply the remaining numbers.

${\tt \leadsto 100 \times 6 = \underline{600}}$

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Simple Interest (2) :-

${\tt \leadsto \underline{\boxed{\tt \dfrac{P \times R \times T}{100}}}}$

Substitute the given values.

${\tt \leadsto \dfrac{8000 \times 5 \times 1}{100}}$

Cancel the zeros in numerator and denominator.

${\tt \leadsto \dfrac{80 \cancel{00} \times 5 \times 1}{1 \cancel{00}} = \dfrac{80 \times 5 \times 1}{1}}$

Multiply the remaining numbers.

${\tt \leadsto 80 \times 5 = \underline{400}}$

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Simple Interest (3) :-

${\tt \leadsto \underline{\boxed{\tt \dfrac{P \times R \times T}{100}}}}$

Substitute the given values.

${\tt \leadsto \dfrac{6000 \times 4 \times 1}{100}}$

Cancel the zeros in numerator and denominator.

${\tt \leadsto \dfrac{60 \cancel{00} \times 4 \times 1}{1 \cancel{00}} = \dfrac{60 \times 4 \times 1}{1}}$

Multiply the remaining numbers.

${\tt \leadsto 60 \times 4 = \underline{240}}$

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Now, let's find the average of all the obtained answers.

Average of all simple interest :-

${\tt \leadsto \underline{\boxed{\tt \dfrac{Sum \: of \: all \: values}{Number \: of \: values}}}}$

Substitute the given values.

${\tt \leadsto \dfrac{600 + 400 + 240}{3}}$

Add all the numbers in numerator.

${\tt \leadsto \dfrac{1240}{3}}$

Simplify the obtained fraction.

${\tt \leadsto \cancel \dfrac{1240}{3} = \pink{\underline{\boxed{\tt 413.33}}}}$

$\Huge\therefore$ The average rate of simple interest is 413.33.

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$\dashrightarrow$ Some related formulas :-

$\small\boxed{\begin{array}{cc}\large\sf\dag \: {\underline{More \: Formulae}} \\ \\ \bigstar \: \sf{Principle :- \dfrac{SI \times 100}{R \times T}} \\ \\\bigstar \: \sf{Rate \: of \: Interest :- \dfrac{SI \times 100}{P \times T}} \\ \\ \bigstar \: \sf{Time :- \dfrac{SI \times 100}{P \times R}}\end{array}}$