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Solved Examples(Set 8) - Simple Interest

36. Sam takes a loan of $₹500$ for his business on $3\text{rd}$ May $2001.$ He had to pay the amount with $6\%$ rate of interest on $15\text{th}$ July $2001.$ What is the simple interest to be paid?
A. $₹9$B. $₹8$
C. $₹4$D. $₹6$
Discuss
answer with explanation

Answer: Option D

Explanation:

Time from $3\text{rd}$ May $2001$ to $15\text{th}$ July $2001$
$=28$ days of May + $30$ days of June + $15$ days of July
$=73$ days $=\dfrac{73}{365}$ years $=\dfrac{1}{5}$ years

Note: Since $3\text{rd}$ May $2001$ is the starting date, it is not included in the counting.

Simple interest $=\dfrac{500×6×\dfrac{1}{5}}{100}=6$

37. Find the simple interest on $₹7500$ at $11\%$ for $2$ years and $5$ months.
A. $₹1994.25$B. $₹1993.75$
C. $₹1991.25$D. $₹1992.75$
Discuss
answer with explanation

Answer: Option B

Explanation:

T $=2$ years $5$ months $=29$ months $=\dfrac{29}{12}$ years

SI $=\dfrac{7500×11×\dfrac{29}{12}}{100}=1993.75$

38. Arun borrowed a sum for $4$ years on simple interest at $12\%.$ The total interest paid was $₹360.$ Find the principal.
A. $₹650$B. $₹800$
C. $₹750$D. $₹700$
Discuss
answer with explanation

Answer: Option C

Explanation:

$\text{P}=\dfrac{100×360}{12×4}=750$
39. What is the simple interest on a loan of $₹1820,$ if it is taken on March $9,2003$ and to be paid back with simple interest on May $21,2003$ at $7\dfrac{1}{2}\%$ rate?
A. $₹22.50$B. $₹27.30$
C. $₹28.80$D. $₹29$
Discuss
answer with explanation

Answer: Option B

Explanation:

Time from March $9,2003$ to May $21,2003$
$=22$ days of March $+30$ days of April $+21$ days of May
$=73$ days $=\dfrac{73}{365}$ years $=\dfrac{1}{5}$ years

Note: Since March $9,2003$ is the starting date, it is not included in the counting.

Rate $=7\dfrac{1}{2}\%=\dfrac{15}{2}\%$

$\text{SI}=\dfrac{1820×\dfrac{15}{2}×\dfrac{1}{5}}{100}=27.30$

40. At what rate percent of simple interest will a sum of money double itself in $20$ years?
A. $6\%$B. $8\%$
C. $5\%$D. $4\%$
Discuss
answer with explanation

Answer: Option C

Explanation:

Solution 1

Let sum be $x$

T $=20$ years

Since the money doubles, simple interest $=x$

$\text{R}=\dfrac{100×\text{SI}}{\text{PT}}=\dfrac{100×x}{x×20}=5$

Solution 2

If rate of interest is $100\%,$ money doubles in $1$ year.

If rate of interest is $\left(\dfrac{100}{20}\right)\%,$ money doubles in $20$ years. That is, required interest rate is $5\%$

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