Verified answer

★Answer :-

• First Part is Rs. 10,800 .
• Second Part is Rs. 6,300 .

★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 :-

★Assume :-

• Let the First Part be x .
• Let the Second Part be 17100 - x .

Also , here two cases are given . So, Let's Solve Case I First .

★Case I :-

Given :-

• Principal be x .
• Time is 3 years .
• Rate of Interest be 7% Per annum .

So , S.I.

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

Here , P represents Principal .

R represents Rate .

T represents Time .

S.I. represents Simple Interest .

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

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

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

★ Case II :-

Given :-

• Principal be 17100 - x .
• Time is 4 years .
• Rate of Interest is 9% Per annum .

So , S.I.

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

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

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

Now ,

★According To The Question :-

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

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

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

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

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

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

[tex]\rm \: \implies { 19x} = 12 \times \: {17100 }[/tex]

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

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

[tex]\rm \: \implies { x} = \bf \: 10800 \bigstar[/tex]

Hence ,

• First Part is Rs. 10800 .
• Second Part is Rs. ( 17,100 - 10,800 ) = Rs. 6,300 .

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