Question

Amit borrowed Rs 2000 from his friend at a Simple Interest 15% per annum.At the end of 2 years and 3 months he settled the load after paying Rs. 16000 and a gold Chain.
Find the cost of the gold chain.​

Answer 1

➤ Correct Question :-

Amit borrowed Rs 2000 from his friend at a Simple Interest 15% per annum.At the end of 2 years and 3 months he settled the load after paying Rs. 1600 and a gold Chain. Find the cost of the gold chain.

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➤ Given :-

Principle :- ₹2000

Rate of interest :- 15%

Time :- 2 years 3 months = 2¼ years

Paid amount :- ₹1600

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➤ To Find :-

The cost of a gold chain.

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➤ Formula required :-

${\large \dashrightarrow \orange{\boxed{\tt \gray{Total \: Amount - Paid \: Amount}}}}$

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★ How to do :-

Here, we are given with the principle amount, the rate of interest, the time taken to return the money back and the amount paid in cash at end of the period. He also gives a gold chain with that cash. We are asked to find the cost of that chain. So, first we should find the simple interest by multiplying the principle, rate and time and then divide it by 100. The obtained answer will be the simple interest. Next, we should add the simple interest and the principle to get total amount. Later, we can find the cost of chain by using the given formula.

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➤ Solution :-

Simple Interest :-

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

Substitute the values.

${\tt \leadsto \dfrac{2000 \times 15 \times 9}{100 \times 4}}$

Cancel the zeros in numerator and denominator.

${\tt \leadsto \dfrac{20 \cancel{00} \times 15 \times 9}{1 \cancel{00} \times 4}}$

Write the resulting statement.

${\tt \leadsto \dfrac{\cancel{20} \times 15 \times 9}{\cancel{4}} = \dfrac{5 \times 15 \times 9}{1}}$

Now, multiply the numbers.

${\tt \leadsto 5 \times 15 \times 9 = \boxed{\tt 675}}$

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Now, find the total amount by adding the simple interest and the principle amount.

Total Amount :-

${\tt \leadsto 675 + 2000}$

${\tt \leadsto Rs \: \: 2675}$

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Now, find the cost of the gold chain by using the given formula.

Cost of the gold chain :-

${\tt \leadsto 2675 - 1600}$

${\tt \leadsto \pink{\underline{\boxed{\tt Rs \: \: 1075}}}}$

$\Huge\therefore$ The cost of the gold chain is ₹1075.

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$\dashrightarrow$ Some related formulas :-

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