Question

A sum of lent out at S.I amount to Rupees 3192 in 3 yrs. and to rupees 3720 in 5 yrs. Find the sum and rate of interest....
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Answer 1

Amount after 2 years =Rs.783

Amount after 3 years =Rs.837

Therefore,

S.I. of 1 year =837−783=Rs.54

⇒ S.I. of 2 years =54×2=Rs.108

Principal sum =783−108=Rs.675

Therefore,

S.I.=100PRt

⇒54=100675×R×1

⇒R=67554×100=8%

Answer 2

Answer :-

Principal is Rs 2,400 and Rate of Interest is 11% .

Note :-

We can calculate SI by using formula ,

$\boxed{\sf SI =\dfrac{P\times R\times T }{100}}$

Also ,there is a another kind of interest called Compound Internet . It can be calculated using,

$\boxed{\sf CI =P\bigg(1+\dfrac{R}{100}\bigg)^n-P}$

The difference between CI and SI is that , in SI Principal remains same every year but in CI , Amount for first year becomes Principal for next year .

Explanation :-

Given that , A sum of lent out at S.I amount to Rupees 3192 in 3 yrs. and to rupees 3720 in 5 yrs. So , let us take the sum be p and rate of interst be r.

$\underline{\red{\sf According\: to\: Question :-}}$

Amount of 5 yrs is Rs 3720 and Amount of 3 yrs is Rs 3192 .

$\sf => Amount\:of\:5\:years\:-(Amount\:of\:3\: years)= Rs 3720 - Rs 3192 \\\\\boxed{\bf=> SI \:of\:2\:yrs\:= Rs 528 }$

$\underline{\red{\sf On\: Using\: Unitary\: method:-}}$

$\sf=> If\:SI\:of\:2\:yrs\:is\:Rs\:528.\\\sf=> Then,\:SI\:of\:1\:year=\dfrac{Rs528}{2}\\\sf=> So,\:the\:SI\:of\:3\:years =\bigg(\dfrac{Rs 528}{2}\bigg)\times 3 \\\boxed{\bf => SI\:of\:3\: years\:=\:Rs792}$

Now , SI for 3 yrs is Rs 792 and Amount is Rs 3192 . Hence the Principal will be Rs 3192 - Rs 792 = Rs 2400

$\underline{\red{\sf Calculating\:Rate\:of\:Interest:-}}$

$\sf=> SI_3 = \dfrac{(P)(R)(T)}{100}\\\\\sf=> Rs 792=\dfrac{Rs 2400\times 3\times R }{100}\\\\\sf=> R = \dfrac{792\times 100}{2400\times 3}\\\\\\\boxed{\bf => Rate \:of\: Interest= 11\%}$

Hence the Principal is Rs 2,400 and the Rate of Interest is 11% .