Math, asked by rahul7654, 1 year ago

A sum of money doubles itself in 8 years. What is the rate of intrest? answer in process.

Answers

Answered by sunita7999
2
let the principal be P
then simple interest will be P
then,
rate=SI×100/P×T
Answered by TRISHNADEVI
3

 \huge{ \underline{ \overline{ \mid{ \mathfrak{ \purple{ \:   \: SOLUTION \:  \: } \mid}}}}}

  \huge{\underline{ \mathfrak{ \green{ \:  \: Method \:  \:    \: 1 \:  : \mapsto \: }}}}

 \underline{ \mathfrak{ \: Given, \: }} \\  \\  \text{ \pink{A sum of money become double of itself}} \\  \text{ \pink{ in 8 years under simple interest.}} \\  \\  \underline{ \mathfrak{ \:Suppose, \: }} \\  \\  \text{ \red{Rate of interest = r }} \\  \\\text{ \red{ Principal = P }} \\  \\ \text{ \red{Amount, A = 2P}} \\  \\  \sf{ \blue{\therefore \:  Simple \:  \:  Interest  = Amount - Principal }} \\   \\ \sf{ \blue{\implies S.I. = 2P - P }} \\  \\   \:  \:  \:  \:  \:  \:  \:  \:  \: \sf{ \blue{\therefore \:  S.I. = P}} \\  \\   \:  \:  \:  \: \text{ \red{Time, n = 8 years.}}

 \underline{ \mathfrak{ \:  \: We \:  \:  know \:  \:  that, \:  \: }} \\  \\  \:  \:  \:  \: \:  \:  \:  \:  \:  \:  \:   \tt{S.I. = \frac{P \times r \times n}{100}} \\ \\   \tt{ \implies \:P =  \frac{P \times r \times 8}{100}  } \\  \\ \tt{ \implies \: 100 \times P = P \times r \times 8 }\\  \\  \tt{ \implies \:P \times r \times 8 = 100 \times P} \\  \\  \tt{ \implies \:r \times 8 =  \frac{100 \times  \cancel{P}}{ \cancel{P}} } \\  \\  \tt{ \implies \:r \times 8 = 100} \\  \\ \tt{ \implies \: r =  \frac{100}{8}  }\\  \\ \:  \:  \:  \:  \:  \:  \:  \tt{ \therefore \:  \:  r = 12.5}

 \:  \:  \:  \:  \sf{ \therefore \: \:   \red{Rate \:  \:  of  \:  \: interest, r =  \underline{ \: 12.5\% \: }}}

 \underline{ \underline{ \:  \: \:  \:  \:   \:  \:  \:  \:  \:  \:  \: \:  \:\: \:  \:  \:  \: \:  \:   \:  \:  \:  \:  \:  \:  \: \:  \:  \:  \:  \:  \:  \:  \:  \: \:  \: \:  \:  \:  \:  \:  \:  \: \:  \:  \:  \:  \:  \:  \:  \:  \: \:  \:   \:  \:  \:  \:  \:  \:  \: \:  \:  \:  \:  \:  \:  \:  \:  \:   \:  \:  \:  \:  \:  \:  \: \:  \: \: \:  \: \:  \:\:  \:  \:   \:  \:  \:  \:   \: \:  \:  \: \:  \:\: \:  \:  \:  \:  \:  \:  \:  \:  \:  \: \:  \: }}

  \huge{\underline{ \mathfrak{ \green{ \:  \: Method \:  \:    \: 2 \:  : \mapsto \: }}}}

 \underline{ \mathfrak{ \: Given, \: }} \\  \\  \text{ \pink{A sum of money become double of itself}} \\  \text{ \pink{ in 8 years under simple interest.}} \\  \\  \underline{ \mathfrak{ \:Suppose, \: }} \\  \\  \text{ \red{Rate of interest = r }} \\  \\  \:  \:  \:  \: \text{ \red{Time, n = 8 years.}} \\  \\ \text{ \red{ Principal , P =Rs. 100 }} \\  \\ \text{ \red{Amount, A = Rs. 200}} \\  \\  \sf{ \blue{\therefore Simple \:  \:  Interest  = Amount - Principal }} \\   \\ \sf{ \blue{\implies S.I. = Rs.(200- 100 )}} \\  \\   \:  \:  \:  \:  \:  \:  \:  \:  \: \sf{ \blue{\therefore \:  \:  S.I. = Rs. 100}}

 \underline{ \mathfrak{ \:  \: We \:  \:  know \:  \:  that, \:  \: }} \\  \\  \:  \:  \:  \: \:  \:  \:  \:  \:  \:  \:   \tt{S.I. = \frac{P \times r \times n}{100}} \\ \\   \tt{ \implies \:100 =  \frac{ \cancel{100} \times r \times 8}{ \cancel{100}}  } \\  \\  \tt{ \implies \:100 =  r \times 8 } \\  \\ \tt{ \implies \: r =  \frac{100}{8}  }\\  \\ \:  \:  \:  \:   \tt{ \therefore \:  \:  r = 12.5}

 \:  \:  \:  \:  \sf{ \therefore \: \:   \red{Rate \:  \:  of  \:  \: interest, r =  \underline{ \: 12.5\% \: }}}

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