Question

-.A sum of Rs. 1500 is lent out in
two parts in such a way that the
simple interest on one part at
10% per annum for 5 years is
equal to that on another part at
12.5% per annum for 4 years.
The sum lent out at 12.5% is :
(in Rs.)​

Answer 1

AnswEr :

Let the First Part be Rs. x which is given at 12.5% p.a. and Second Part be Rs. (1500 - x) given at 10% p.a.

$\bold{First \: Part} \begin{cases} \sf{Principal=Rs. x} \\ \sf{Rate=12.5\% \: p.a.} \\ \sf{Time=4 \: Yr.}\end{cases}$

$\bold{Second \: Part} \begin{cases} \sf{Principal=Rs. (1500 - x)} \\ \sf{Rate=10\% \: p.a.} \\ \sf{Time=5 \: Yr.}\end{cases}$

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• According to the Question Now :

$\Longrightarrow \large\sf {Simple \: Interest_1 =Simple \: Interest_2 }$

$\Longrightarrow \large\sf\dfrac{(PRT)_1}{ \cancel{100}} = \dfrac{(PRT)_2}{\cancel{100}}$

$\Longrightarrow \large\sf (PRT)_1= (PRT)_2$

⠀⠀⠀⠀⋆ Plugging the Values

$\Longrightarrow \sf{(x \times 12.5 \times 4) = (1500 - x) \times 10 \times 5}$

$\Longrightarrow \large \sf{50x = (1500 - x) \times 50}$

$\Longrightarrow \large \sf{\dfrac{\cancel{50}x}{\cancel{50}}= (1500 - x)}$

$\Longrightarrow \large \sf{x = 1500 - x}$

$\Longrightarrow \large \sf{x + x = 1500}$

$\Longrightarrow \large \sf{2x = 1500}$

$\Longrightarrow \large \sf{x = \cancel\dfrac{1500}{2} }$

$\Longrightarrow \large \boxed{\sf{x = Rs.\: 750}}$

⠀

჻ The sum lent out at 12.5% p.a. is Rs. 750.

Answer 2

Step-by-step explanation:

Let the First Part be Rs. x which is given at 12.5% p.a. and Second Part be Rs. (1500 - x) given at 10% p.a.

\begin{gathered}\bold{First \: Part} \begin{cases} \sf{Principal=Rs. x} \\ \sf{Rate=12.5\% \: p.a.} \\ \sf{Time=4 \: Yr.}\end{cases}\end{gathered}FirstPart⎩⎪⎪⎨⎪⎪⎧Principal=Rs.xRate=12.5%p.a.Time=4Yr.

\begin{gathered}\bold{Second \: Part} \begin{cases} \sf{Principal=Rs. (1500 - x)} \\ \sf{Rate=10\% \: p.a.} \\ \sf{Time=5 \: Yr.}\end{cases}\end{gathered}SecondPart⎩⎪⎪⎨⎪⎪⎧Principal=Rs.(1500−x)Rate=10%p.a.Time=5Yr.

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• According to the Question Now :

\Longrightarrow \large\sf {Simple \: Interest_1 =Simple \: Interest_2 }⟹SimpleInterest1=SimpleInterest2

\Longrightarrow \large\sf\dfrac{(PRT)_1}{ \cancel{100}} = \dfrac{(PRT)_2}{\cancel{100}}⟹100(PRT)1=100(PRT)2

\Longrightarrow \large\sf (PRT)_1= (PRT)_2⟹(PRT)1=(PRT)2

⠀⠀⠀⠀⋆ Plugging the Values

\Longrightarrow \sf{(x \times 12.5 \times 4) = (1500 - x) \times 10 \times 5}⟹(x×12.5×4)=(1500−x)×10×5

\Longrightarrow \large \sf{50x = (1500 - x) \times 50}⟹50x=(1500−x)×50

\Longrightarrow \large \sf{\dfrac{\cancel{50}x}{\cancel{50}}= (1500 - x)}⟹5050x=(1500−x)

\Longrightarrow \large \sf{x = 1500 - x}⟹x=1500−x

\Longrightarrow \large \sf{x + x = 1500}⟹x+x=1500

\Longrightarrow \large \sf{2x = 1500}⟹2x=1500

\Longrightarrow \large \sf{x = \cancel\dfrac{1500}{2} }⟹x=21500

\Longrightarrow \large \boxed{\sf{x = Rs.\: 750}}⟹x=Rs.750