Question

Simple interest on 500 at a certain rate for 2 years is 100. Find the simple interest of the same amount of money, at the same rate for 5 years.
(A) 110
(B) 150
(C) 250
(D) 300​

Answer 1

Given:

• Simple interest on 500 at a certain rate for 2 years is 100.

To Find:

• the simple interest of the same amount of money, at the same rate for 5 years.

Solution:

We know that,

${ \boxed{\sf{\purple{ \: simple \: interest = \frac{p \times t \times r}{100} }}}}\bigstar$

Now let's substitute the values to find the Rate of interest

$\sf \: { : \implies}100 = \frac{500 \times 2 \times r}{100} \\ \\ \\ \sf \: { : \implies}100 = \frac{ 10\cancel{00} \times r} {\cancel{{100} }} \\ \\ \\\sf \: { : \implies}100 = 10 \times r \\ \\ \\ \sf \: { : \implies}r\: = \cancel\frac{100}{10} \\ \\ \\ \sf \: { : \implies}{ \boxed {\purple {\sf{r = 10\%}}}} \bigstar$

$\rm \therefore {\underline{rate \: of \: intrest = 10\%p.a }}$

Now let's find the simple interest for 5 years.!

$\\ \\ \\ \\ \sf \: { : \implies} \:S . I= \frac{p \times t \times r}{100} \\ \\ \\ \sf \: { : \implies}S . I = \frac{ \cancel{500} \times 5 \times 10} {\cancel{{100} }} \\ \\ \\ \sf \: { : \implies}Simple \: interest= r.s250 \bigstar$

$\blue{ \underline{ \boxed{ \pink{ \mathfrak{ \therefore \:simple \: interest \: for \: 5 \: years = 250}}}}}$

Answer 2

Given :-

• Simple interest on 500 at a certain rate for 2 years is 100.
• Principal = Rs,500
• Time = 2 years
• Simple Interest = Rs,100

To Find :-

• The simple interest of the same amount of money, at the same rate for 5 years.

Solution :-

➞ Simple Interest = P × R × T ÷ 100

➞ 100 = 500 × R × 2 ÷ 100

➞ 100 = 5 × R × 2

➞ 100 = 10 × Rate

➞ 100 ÷ 10 = Rate

➞ 10% = Rate

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➞ Simple Interest = P × R × T ÷ 100

➞ Simple Interest = 500 × 10 × 5 ÷ 100

➞ Simple Interest = 5 × 10 × 5

➞ Simple Interest = 25 × 10

➞ Simple Interest = Rs,250

Therefore, Correct Option is C i.e Rs,250

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★ Additional Info :

• Principal: The money which we deposit in or the lower from the bank or the money learned called the principal.
• Rate of interest: The interest paid on Rs, 100 for one year is called the rate per cent per year or rate per cent per annum.
• Time: The period of time for which the money is lent or invested.
• Interest: Additional money paid by the borrowed to the lender for using the money is called interest.
• Simple Interest: If the interest is calculated uniformly on the original principal throughout the lone period, it is called simple interest.
• Amount: The total money paid back to the lender is called the amount.

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