Question

The principal and interest for 5 years are together Rs2142 and the interest is 9/25 of the principal. Find the principal and the rate of interest.​

Answer 1

Explanation:

Hope it helps uu.......

Answer 2

Answer:

★ Principal = Rs. 1575 ★

★ Rate of interest = 7.2% ★

Explanation:

Given:

• The principal and interest for 5 years are in together Rs. 2142 and the interest is 9/25 of the principal.

To find:

• The principal and rate of interest.

Solution:

We know that,

★ ${\boxed{\sf{Simple\: Interest=\dfrac{ptr}{100}}}}$

Here,

• p = Principal
• t = time = 5 years
• r = rate of interest

★According to the 1st condition:-

• The principal and interest for 5 years are in together Rs. 2142.

$\implies\sf{p+\dfrac{ptr}{100}=2142}$

$\implies\sf{p+\dfrac{p\times\:5\times\:r}{100}=2142}$

$\implies\sf{p+\dfrac{5pr}{100}=2142..........(i)}$

★According to the 2nd condition:-

• The interest is 9/25 of the principal.

$\implies\sf{\dfrac{ptr}{100}=p\times\dfrac{9}{25}}$

$\implies\sf{\dfrac{5pr}{100}=\dfrac{9p}{25}.............(ii)}$

Now put 5pr/100 = 9p/25 in eq(i).

$\mapsto\sf{p+\dfrac{5pr}{100}=2142}$

$\mapsto\sf{p+\dfrac{9p}{25}=2142}$

$\mapsto\sf{\dfrac{34p}{25}=2142}$

$\mapsto\sf{34p=53500}$

$\mapsto\sf{p=1575}$

Therefore, the principal is Rs. 1575.

Now put p = 1575 in eq(ii).

$\implies\sf{\dfrac{5pr}{100}=\dfrac{9p}{25}}$

$\implies\sf{\dfrac{r}{20}=\dfrac{9}{25}}$

$\implies\sf{r=\dfrac{9}{25}\times\:20}$

$\implies\sf{r=\dfrac{36}{5}}$

$\implies\sf{r=7.2}$

Therefore, the rate of interest is 7.2%.