Question

two equal sum of money were lent at simple interest at 11% p.a.for 3 1/2 years and 4 1/2 years respectively. if the difference in interest two period was ₹41250,then each sum was​

Answer 1

AnswEr :

Let the Equal Sum of money be Rs. x

$\bold{First \: Part} \begin{cases} \sf{Principal=Rs. x} \\ \sf{Rate=11\% \: p.a.} \\ \sf{Time=4 \dfrac{1}{2} \: = 4.5 \: Yr. }\end{cases}$

$\bold{Second \: Part} \begin{cases} \sf{Principal=Rs. x} \\ \sf{Rate=11\% \: p.a.} \\ \sf{Time=3 \dfrac{1}{2} \: =3.5 \: Yr. }\end{cases}$

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$\longrightarrow \large \sf{Difference = SI_1 - SI_2}$

$\longrightarrow \sf{Diff. = \dfrac{PRT_1}{100} - \dfrac{PRT_2}{100}}$

$\longrightarrow \sf{41250 = \dfrac{x \times 11 \times 4.5}{100} - \dfrac{x \times 11 \times 3.5}{100}}$

$\longrightarrow \sf{41250 = \dfrac{49.5x}{100} - \dfrac{38.5x}{100} }$

$\longrightarrow \sf{41250 = \dfrac{(49.5x - 38.5x)}{100}}$

$\longrightarrow \sf{ \cancel{41250} = \dfrac{ \cancel{11}x}{100}}$

$\longrightarrow \sf{3750 = \dfrac{x}{100}}$

$\longrightarrow \sf{3750 \times 100 = x}$

$\longrightarrow \large \sf{x =Rs. 375000}$

⠀

$\therefore$ Equal Sum is Rs. 3,75,000.

Answer 2

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