Question

A Certain sum was lent at simple interest for 9 years. it amounted to 19,200 at the end of 6 years and at end of 9 years it amounted to 22,800 find sum and rate of interest​

Answer 1

Answer:

8=7:45$@2457-$!':'75#!

Answer 2

Concept Introduction:-

It may be in the form of a word, a symbol, or a figure that reflects the arithmetic value of a quantity.

Given Information:-

We have been given that a Certain sum was lent at simple interest for $9$ years. it amounted to $19,200$ at the end of $6$ years and at end of $9$ years it amounted to $22,800$.

To Find:-

We have to find that the sum and rate of interest​.

Solution:-

According to the problem

Amount after $6$ years, $A=P+(P \times R \times T) / 100$

$19200=P+6 P R / 100....(i)$

Amount after $9$ years,

$22800=P+9 P R / 100......(ii)$

Subtract $(i)$ from $(ii)$, we get

$3600=3 \mathrm{PR} / 100$

$\therefore 6 \mathrm{PR} / 100=7200$

Now, put $6 \mathrm{PR} / 100=7200$ in eq $(i)$

$19200=P+6 P R / 100\\\therefore P=19200-7200=12000$

Putting the value of P in equation  $(i)$

$19200=12000+6 \times 12000 R / 100\\\therefore 19200-12000=72000R/100\\\therefore 7200=72000R/100\\\therefore 7200\times 100=72000R\\\therefore 7200\times 100=72000R\\\therefore \frac{720000}{72000}=R\\\therefore R=10\%$

Final Answer:-

The sum and rate of interest are Rs. $12000$ and $10\%$ respectively.

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