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Divide 17,100 into two parts such that the simple interest on the first part for 3 years at 7% per annum is equal to the simple interest on the second part for 4 year at 9% per annum.


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Sagot :

MasterOfMathProblemidn

Understanding Question Properly !!

  • Divide 17,100 into two Parts such that Simple Interest on First Part for 3 years at 7% Per annum is equal to Simple Interest on Second Part for 4 years at 9% Per annum .

Here , First we need to assume the two Parts . Then , Just Calculate with Formula :-

[tex]\tt \: Assume :- \\ \tt Let \: \: the \: \: First \: \: Part \: \: be \: \: x . \\ \tt Let \: \: the \: \: Second \: Part \: \: be \: \: 17100 - x . \\ \tt \: Also , \: \: here \: \: two \: \: cases \: \: are \: \: given . \\ \tt \: So, \: Let's \: Solve \: Case \: I \: First .[/tex]

  • [tex]\tt \: S.I. = \dfrac{ P \times R \times T}{100}[/tex]

  • [tex] \tt\: \implies S.I. = \dfrac{ x \times 7\times 3}{100}[/tex]

  • [tex] \tt \: \implies S.I. = \tt \dfrac{21x}{100}[/tex]

  • [tex] \tt \: Hence \: , \: in \: case \: I \: the \: S.I. \: is \: \tt\dfrac{21x}{100} [/tex]

  • [tex] \tt \: S.I. = \dfrac{ P \times R \times T}{100}[/tex]

Already we wrote what P , R and T refers to and Also what S.I. stands for .

  • [tex]\tt \: \implies S.I. = \dfrac{(17100 - x) \times 9\times 4}{100}[/tex]

  • [tex]\tt\: \implies S.I. = \dfrac{(17100 - x) \times 36}{100}[/tex]

[tex]\tt\: Hence \: , \: in \: case \: I I \: the \: S.I. \: is \: \tt\dfrac{(17100 - x )\times 36}{100}[/tex]

Now

According To The Question :-

  • [tex]\tt \: \implies \dfrac{21x }{100} = \: \dfrac{(17100 - x) \times 36}{100}[/tex]

L.H.S 100 gets multiplied at the Up of R.H.S . So , it's get divided with other 100 .

  • [tex]\tt \: \implies {21x } = \: \dfrac{(17100 - x )\times 36 \times 100}{100}[/tex]

  • [tex]\tt \: \implies {21x } = \: {(17100 - x) \times 36 }[/tex]

  • [tex]\tt \: \implies {21x } = \: {17100 \times36 - 36x}[/tex]

What Happens next is that with 3 we divide both of this sides

  • [tex]\tt\: \implies {7x } = 12 \times \: {17100 - 12x}[/tex]

  • [tex]\tt \: \implies {7x + 12x} = 12 \times \: {17100 }[/tex]

  • [tex]\tt\: \implies { 19x} = 12 \times \: {17100 }[/tex]
  • [tex]\tt \: \implies { x} = \dfrac{12 \times 17100}{19} [/tex]

  • [tex]\tt \: \implies { x} = {12 \times 900}[/tex]

  • [tex]\tt\: \implies { x} = \tt\: 10800 [/tex]

Hence ,

First Part is Rs. 10800 .

Second Part is Rs. ( 17,100 - 10,800 ) = Rs. 6,300 .

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[tex]\qquad\qquad\qquad\qquad\qquad\qquad\tt{03-02-2022} \\ \qquad\qquad\qquad\qquad\qquad\qquad\tt{1:56 \: pm}[/tex]

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