Question

81) Divide Rs 12,000 in two parts so that the interest on one part at 12.5% for 4 years is
equal to the interest on the second part at 10% for 3 years.
a) Rs 4500, Rs 7000
b) Rs 4500, Rs 7500
c) Rs 4500, Rs 7000
d) Rs 4500, Rs 7000​

Answer 1

Given :-

$\sf\bullet {Total ( \ P_{1}+ \ P_{2})\:=\:12,000}$

①

$\sf{Rate \ ( R_{1})\:=\:12.5 }$ %

$\sf{Time \ ( T_{1})\:=\:4years }$

②

$\sf{Rate \ ( R_{2})\:=\:10 }$ %

$\sf{Time \ ( T_{2})\:=\:3years}$

To find :-

$\mathrm{ \ P_{1} \: and \: \ P_{2}}$

Formula used !

$\bigstar{\boxed{\sf{\frac{ \ P × R × T}{100}}}}$

Solution :-

$\tt{ \ P_{1}+ \ P_{2}\:=\:12000}$

${Let\: \ P_{1}\:=\:a}$

${Let\: \ P_{2}\:=\:b}$

A.T.Q

${ \frac{ \ P_{1} × \ R_{1} × \ T_{1}}{100} \: = \: \frac{ \ P_{2} × \ R_{2} × \ T_{2}}{100}}$

$\frac{a×12.5×4}{100}\: =\: \frac{(12000-a)×10×3}{100}$

${a×12.5×4=(12000-a)×10×3}$

${ 5a = 36000 - 3a }$

${8a = 36000}$

$\boxed{a = 4500}$

$\boxed{b = 7500}$

$\therefore{ \purple{ \mathrm{ \large{ \underline{ \underline{ So\: Option\:b\:is\: correct}}}}}}$

$\huge\tt{\orange{Thanks}}$

______________________________________

Answer 2

Given : Rs 12,000 invested in two parts so that the interest on one part at 12.5% for 4 years is equal to the interest on the second part at 10% for 3 years.

To find : Each part

Solution:

Let Say Amount invested at  12.5%  for 4 years = A

then Amount invested at  10%  for 3 years = 12000 - A

Interest on A  =  A * 12.5  * 4 / 100  = A/2

interest on 12000 - A  =   (12000 - A) * 10 * 3/100  = 3600 - 3A/10

A/2 = 3600 - 3A/10

=> A/2 + 3A/10  = 3600

=> 5A  + 3A = 36000

=> 8A = 36000

=> A = 4500

one part = 4500

Another Part = 12000 - 4500 = 7500

option b    Rs 4500, Rs 7500   is correct

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