A sum of 5000 is divided into two parts

Asked by admin @ 12/08/2021 in Math viewed by 302 People

11. Divide 5000 into two parts such that the simple interest on the first part for 2 years at 10%

per annum is equal to the simple interest on the second part for 3 years at 20% per annum.

Answered by admin @ 12/08/2021

AnswEr :

Let the First Part be Rs. x and Second Part be Rs. (5,000 - x).

$\bold{First \: Part} \begin{cases} \sf{Principal=Rs. x} \\ \sf{Rate=10\% \: p.a.} \\ \sf{Time=2 \: Yr.}\end{cases}$

$\bold{Second \: Part} \begin{cases} \sf{Principal=Rs. (5,000 -x)} \\ \sf{Rate=20\% \: p.a.} \\ \sf{Time=3 \: Yr.}\end{cases}$

• According to Question Now ;

$\leadsto\sf{SI_1 = SI_2}$

$\leadsto\sf{\dfrac{PRT_1}{\cancel{100}}=\dfrac{PRT_2}{\cancel{100}}}$

Using the Values Now

$\leadsto \sf{x \times 10 \times 2 = (5000 - x) \times 20 \times 3}$

$\leadsto \sf{20x = 300000 - 60x}$

$\leadsto \sf{20x + 60x= 300000}$

$\leadsto \sf{80x = 300000 }$

$\leadsto \sf{x = \cancel\dfrac{300000}{80} }$

$\leadsto$ Rs. 3,750

• Second Part be :

⇒ Rs. (5,000 - x)

⇒ Rs. (5,000 - 3,750)

⇒ Rs. 1,250

⠀

$\therefore$ Rs. 3750 and Rs. 1250 is two different Part on which Simple Interest will be Equal.

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