Question

The simple interest on a certain sum for 8 months at 4% simple interest is Rs 129 less than the simple interest on the same sum for 15 months at 5% per annum. Then the sum is ?

Answer 1

Answer:

₹3600

Explanation:

Let's say that the sum is x

Then, simple interest on x for 8 months at 4% is 129 less than the simple interest on x for 15 months at 5% per annum.

Case (i) :-

Simple interest is given by :-

$\sf = \dfrac{p \times r \times t}{100}$

Where,

• p(principal) = x
• r(rate) = 4%
• t(time) = 8 months or, 2/3 years.

So,

$\sf = \dfrac{x \times 4 \times 2}{100 \times 3}$

$\sf = \dfrac{8x}{300}$

Case (ii) :-

Calculating simple interest on,

• p = x
• r = 5%
• t = 15 months or, 5/4 years.

So,

$\sf = \dfrac{x \times 5 \times 5}{100 \times 4}$

$\sf = \dfrac{25x}{400}$

According to the question,

The amount $\sf \dfrac{8x}{300}$ is less than $\sf \dfrac{25x}{400}$ by 129.

Equation forms :

$\sf \implies \: \dfrac{25x}{400} - \dfrac{8x}{300} = 129$

$\sf \implies \: \dfrac{75x - 32x}{1200} = 129$

$\sf \implies \: \dfrac{43x}{1200} = 129$

$\sf \implies \: x = \dfrac{129 \times 1200}{43}$

$\sf \implies \: x = 3600$

∴ The sum is ₹3600