Question

The simple interest on a certain sum at 5% per annum for 3 years and 4 years differ by
82. Find the sum

Answer 1

Answer:

The amount is 1640.

Step-by-step explanation:

The formula to find simple interest on a sum of P is,

$I=\frac{PNR}{100}$

where N is the number of years and R is the annual rate of interest.

Here the difference between the interest for 3 years and 4 years is given. The interest rate is 5% per annum. So we get the equation,

$\dfrac{P\times 4\times 5}{100}- \dfrac{P\times 3\times 5}{100}=82$

We can solve the above equation to get the value of P.

$\implies \dfrac{20P}{100}-\dfrac{15P}{100}=82\\\\\implies 20P-15P=8200\\\\\implies 5P=8200\\\\\implies P=\dfrac{8200}{5}= 1640$

Answer 2

Answer:

Given :-

• The simple interest on a certain sum at 5 % per annum for 3 Years and 4 Years differ by 82 .

To Find :-

• What is the sum.

Formula Used :-

$\clubsuit$ Simple Interest or S.I Formula :

$\bigstar \: \: \sf\boxed{\bold{\pink{S.I =\: \dfrac{P \times r \times t}{100}}}}\: \: \: \bigstar$

where,

• S.I = Simple Interest
• P = Principal
• r = Rate of Interest
• t = Time Period

Solution :-

Let,

$\mapsto \bf Sum =\: Rs\: x$

$\sf\bold{\underline{\purple{\clubsuit\: In\: the\: first\: case\: :-}}}$

Given :

• Principal = Rs x
• Rate of Interest = 5% per annum
• Time Period = 3 years

According to the question by using the formula we get,

$\implies \sf S.I =\: \dfrac{x \times 5 \times 3}{100}$

$\implies \sf S.I =\: \dfrac{x \times 15}{100}$

$\implies \sf\bold{\blue{S.I =\: \dfrac{15x}{100}\: ------\: (Equation\: No\: 1)}}$

Again,

$\sf\bold{\underline{\purple{\clubsuit\: In\: the\: second\: case\: :-}}}$

Given :

• Principal = Rs x
• Rate of Interest = 5% per annum
• Time Period = 4 years

According to the question by using the formula we get,

$\implies \sf S.I =\: \dfrac{x \times 5 \times 4}{100}$

$\implies \sf S.I =\: \dfrac{x \times 20}{100}$

$\implies \sf\bold{\blue{S.I =\: \dfrac{20x}{100}\: ------\: (Equation\: No\: 2)}}$

Now, according to the question from the equation no 1 and equation no 2 we get :

$\leadsto$ The difference is 82.

So,

$\implies \bf \dfrac{20x}{100} - \dfrac{15x}{100} =\: 82$

$\implies \sf \dfrac{20x - 15x}{100} =\: 82$

$\implies \sf \dfrac{5x}{100} =\: 82$

By doing cross multiplication we get,

$\implies \sf 5x =\: 100 \times 82$

$\implies \sf 5x =\: 8200$

$\implies \sf x =\: \dfrac{\cancel{8200}}{\cancel{5}}$

$\implies \sf x =\: \dfrac{1640}{1}$

$\implies \sf\bold{\red{x =\: Rs\: 1640}}$

$\therefore$ The sum is Rs 1640 .