Question

Simple interest on a certain sum for 4 years at 7% p.a. is more than simple
interest on the same sum for 2.5 years at the same rate by 840. Find the
principal amount.​

Answer 1

Question :-

Simple interest on a certain sum for 4 years at 7% p.a. is more than simple interest on the same sum for 2.5 years at the same rate by 840. Find the principal amount.

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Solution :-

Given Information :-

• ■ Rate 1 ➭ 7% p.a.
• ■ Time 1 ➭ 4 years
• ■ Rate 2 ➭ 7% p.a.
• ■ Time 2 ➭ 2.5 years
• ■ Difference in Interests ➭Rs. 840

To Find :-

• ■ The principal amount.

Formula Used :-

• ■ $\sf Simple Interest = \frac{principal \times rate \times time}{100}$

Calculation :-

Let's assume principal amount as 'P'

Substituting the values, We get,

$\sf: \implies \frac{P \times 7 \times 4}{100} = \frac{ P \times 7 \times 2.5 }{100} + 840$

$\sf: \implies \frac{28 P }{100} = \frac{17.5 P }{100} + 840$

$\small \sf: \implies 0.28P = 0.175P + 840$

$\small \sf: \implies 0.28P - 0.175P = 840$

$\small \sf: \implies 0.105P = 840$

$\small \sf: \implies P = \frac{840}{0.105}$

$\small \bf: \implies P = Rs. \: 8000$

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Final Answer :-

The Principal Amount will be Rs. 8000.

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Answer 2

Step-by-step explanation:

• Given : Simple interest on a certain sum for 4 years at 7% p.a. is more than simple interest on the same sum for 2.5 years at the same rate by 840.

Exigency To Find : The Principal amount.

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❍ Let's Consider the Principal amount be P .

$\begin{gathered}\dag\:\:\sf{ As,\:We\:know\:that\::}\\\\ \qquad\maltese\:\:\bf \:Formula\:for\:Simple\:Interest\:\::\\\end{gathered}†$

$\begin{gathered}\qquad \dag\:\:\bigg\lgroup \sf{Simple \:Interest \:: \dfrac{P \times R \times T}{100} }\bigg\rgroup \\\\\end{gathered}$

⠀⠀⠀⠀⠀Here , P is the Principal, R is the Rate of Interest & T is the Time.

⠀⠀⠀⠀ $\begin{gathered}\underline {\boldsymbol{\star\: According \:to\: the \:Question \::}}\\\end{gathered}$

• ━━━ Simple interest on a certain sum for 4 years at 7% p.a. is more than simple interest on the same sum for 2.5 years at the same rate by 840.

$\begin{gathered}\qquad:\implies \sf 1^{st} \: Simple \:Interest \: = \: 2^{nd} \: Simple \:Interest\:\:+ 840 \\\end{gathered}$

$\begin{gathered}\qquad:\implies \sf \dfrac{ P \times 7 \:\times 4 }{100} = \dfrac{ P \times 7 \:\times 2.5 }{100} + 840 \\\end{gathered}$

$\begin{gathered}\qquad:\implies \sf \dfrac{ P \times 28 }{100} = \dfrac{ P \times 17.5 }{100} + 840 \\\end{gathered}$

$\begin{gathered}\qquad:\implies \sf \dfrac{ 28P }{100} = \dfrac{ 17.5P }{100} + 840 \\\end{gathered}$

$\begin{gathered}\qquad:\implies \sf \cancel {\dfrac{ 28P }{100}} = \dfrac{ 17.5P }{100} + 840 \\\end{gathered}$

$\begin{gathered}\qquad:\implies \sf 0.28 \:P = \dfrac{ 17.5P }{100} + 840 \\\end{gathered}$

$\begin{gathered}\qquad:\implies \sf 0.28 \:P = \cancel {\dfrac{ 17.5P }{100}} + 840 \\\end{gathered}$

$\begin{gathered}\qquad:\implies \sf 0.28 \:P = 0.175P + 840 \\\end{gathered}$

$\begin{gathered}\qquad:\ \sf 0.28 \:P- 0.175 P = 840 \\\end{gathered}$

$\begin{gathered}\qquad:\implies \sf 0.105 P = 840 \\\end{gathered}$

$\begin{gathered}\qquad:\implies \sf P = \dfrac{840}{0.015} \\\end{gathered}$

$\begin{gathered}\qquad:\implies \sf P = \cancel {\dfrac{840}{0.015}} \\\end{gathered}$

$\begin{gathered}\qquad:\implies \bf P = 8000 \\\end{gathered}$

$\begin{gathered}\qquad:\implies \rm{\underline{\purple{\:P = Rs.8000 }} }\:\:\bigstar \\\end{gathered}$

Therefore,

⠀⠀⠀⠀⠀ $\begin{gathered}\therefore {\underline{ \mathrm {\:Principal \:amount\:\:is\:\bf{Rs.8000}}}}\\\end{gathered}$

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